##############ECHO OF PROBLEM################# ##############temp/div_c_lin_backpostode.ode################# diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(3.1); x_end=c(2.5); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_display_interval=c(0.1); glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-1.5); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(1.0); array_given_ord_poles[1][2]=c(0.0); /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(20.0); glob_subiter_method=3; glob_max_iter=1000; glob_upper_ratio_limit=c(1.11); glob_lower_ratio_limit=c(0.99); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(10.0)* ln(c(0.2)* c(x) + c(0.3))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (closed_form) = -0.8338160893905089 y[1] (numeric) = -0.8338160893905089 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (closed_form) = -0.725706928348355 y[1] (numeric) = -0.7257069283456293 absolute error = 2.725708547757222e-12 relative error = 3.755935683238817e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 4.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (closed_form) = -0.6187540371808753 y[1] (numeric) = -0.6187540371755972 absolute error = 5.278111281370457e-12 relative error = 8.530225201306524e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 4.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (closed_form) = -0.5129329438755058 y[1] (numeric) = -0.5129329438678337 absolute error = 7.672085189369682e-12 relative error = 1.495728687536158e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 4.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.299999999999999 y[1] (closed_form) = -0.4082199452025517 y[1] (numeric) = -0.4082199451926327 absolute error = 9.919010057757305e-12 relative error = 2.429820045376681e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 4.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.349999999999999 y[1] (closed_form) = -0.3045920748470857 y[1] (numeric) = -0.3045920748350564 absolute error = 1.20293219829648e-11 relative error = 3.94932205278285e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 4.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.399999999999999 y[1] (closed_form) = -0.2020270731751969 y[1] (numeric) = -0.2020270731611821 absolute error = 1.401484484020443e-11 relative error = 6.937112249332458e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 4.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.449999999999999 y[1] (closed_form) = -0.1005033585350167 y[1] (numeric) = -0.1005033585191368 absolute error = 1.587990849927223e-11 relative error = 1.580037595832129e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.05 Radius of convergence (given) for eq 1 = 4.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.499999999999999 y[1] (closed_form) = -2.220446049250313e-15 y[1] (numeric) = 1.763268697718701e-11 absolute error = 1.763490742323626e-11 relative error = 794205.6249999999 % Desired digits = 8 Estimated correct digits = 3 Correct digits = -2 h = 0.05 Radius of convergence (given) for eq 1 = 5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.549999999999998 y[1] (closed_form) = 0.09950330853167871 y[1] (numeric) = 0.09950330855096605 absolute error = 1.928733561751272e-11 relative error = 1.938361236638905e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.05 Radius of convergence (given) for eq 1 = 5.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.599999999999998 y[1] (closed_form) = 0.1980262729617951 y[1] (numeric) = 0.1980262729826393 absolute error = 2.084413197600554e-11 relative error = 1.052594267631698e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.05 Radius of convergence (given) for eq 1 = 5.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.649999999999998 y[1] (closed_form) = 0.29558802241544 y[1] (numeric) = 0.2955880224377538 absolute error = 2.231381746042871e-11 relative error = 7.548958607350916e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.699999999999998 y[1] (closed_form) = 0.3922071315328091 y[1] (numeric) = 0.392207131556507 absolute error = 2.369798801638012e-11 relative error = 6.042212420708554e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.749999999999998 y[1] (closed_form) = 0.4879016416943163 y[1] (numeric) = 0.4879016417193206 absolute error = 2.500433193830531e-11 relative error = 5.1248714498016e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.799999999999998 y[1] (closed_form) = 0.582689081239754 y[1] (numeric) = 0.5826890812659919 absolute error = 2.623790074096632e-11 relative error = 4.502898987765731e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.849999999999997 y[1] (closed_form) = 0.6765864847381444 y[1] (numeric) = 0.6765864847655478 absolute error = 2.740341287221781e-11 relative error = 4.050245384789737e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.899999999999997 y[1] (closed_form) = 0.7696104113612777 y[1] (numeric) = 0.7696104113897848 absolute error = 2.850708558099768e-11 relative error = 3.704093026830898e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.949999999999997 y[1] (closed_form) = 0.8617769624105178 y[1] (numeric) = 0.861776962440067 absolute error = 2.954914091191085e-11 relative error = 3.428861782201456e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.999999999999997 y[1] (closed_form) = 0.9531017980432434 y[1] (numeric) = 0.9531017980737784 absolute error = 3.053501895777799e-11 relative error = 3.203752109215157e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.049999999999997 y[1] (closed_form) = 1.043600153242423 y[1] (numeric) = 1.043600153273891 absolute error = 3.146838345458036e-11 relative error = 3.015367845319819e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.099999999999997 y[1] (closed_form) = 1.133286853070027 y[1] (numeric) = 1.133286853102379 absolute error = 3.235278711599676e-11 relative error = 2.854774766719866e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.149999999999997 y[1] (closed_form) = 1.222176327242487 y[1] (numeric) = 1.222176327275678 absolute error = 3.319078345498383e-11 relative error = 2.715711531565165e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.199999999999997 y[1] (closed_form) = 1.310282624064036 y[1] (numeric) = 1.310282624098021 absolute error = 3.398503700680067e-11 relative error = 2.59371805613899e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.249999999999996 y[1] (closed_form) = 1.39761942375158 y[1] (numeric) = 1.397619423786321 absolute error = 3.474043275275562e-11 relative error = 2.485686171955389e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.299999999999996 y[1] (closed_form) = 1.484200051182726 y[1] (numeric) = 1.484200051218182 absolute error = 3.545541638061422e-11 relative error = 2.38885697061933e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.349999999999996 y[1] (closed_form) = 1.570037488096641 y[1] (numeric) = 1.570037488132776 absolute error = 3.613465082707989e-11 relative error = 2.301515161328154e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.399999999999996 y[1] (closed_form) = 1.655144384775728 y[1] (numeric) = 1.655144384812507 absolute error = 3.677946835978219e-11 relative error = 2.222130510068208e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.449999999999996 y[1] (closed_form) = 1.739533071234374 y[1] (numeric) = 1.739533071271766 absolute error = 3.73925335139802e-11 relative error = 2.14957301659384e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 5.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.499999999999996 y[1] (closed_form) = 1.823215567939538 y[1] (numeric) = 1.823215567977515 absolute error = 3.797695491414288e-11 relative error = 2.082965699830086e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.549999999999995 y[1] (closed_form) = 1.90620359608649 y[1] (numeric) = 1.906203596125021 absolute error = 3.853095620343083e-11 relative error = 2.021345268812649e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.599999999999995 y[1] (closed_form) = 1.988508587451645 y[1] (numeric) = 1.988508587490703 absolute error = 3.905809009552286e-11 relative error = 1.96419016452815e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.649999999999995 y[1] (closed_form) = 2.070141693843254 y[1] (numeric) = 2.070141693882814 absolute error = 3.955991090265343e-11 relative error = 1.91097599842114e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.699999999999995 y[1] (closed_form) = 2.151113796169448 y[1] (numeric) = 2.151113796209486 absolute error = 4.00377508924521e-11 relative error = 1.86125675748761e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.749999999999995 y[1] (closed_form) = 2.231435513142089 y[1] (numeric) = 2.231435513182583 absolute error = 4.049471868938781e-11 relative error = 1.814738469962196e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.799999999999994 y[1] (closed_form) = 2.311117209633858 y[1] (numeric) = 2.311117209674786 absolute error = 4.092859384741132e-11 relative error = 1.770944099105017e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.849999999999994 y[1] (closed_form) = 2.39016900470499 y[1] (numeric) = 2.390169004746333 absolute error = 4.134248499099158e-11 relative error = 1.729688775547247e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.899999999999994 y[1] (closed_form) = 2.46860077931525 y[1] (numeric) = 2.468600779356986 absolute error = 4.173683620933843e-11 relative error = 1.690708216535343e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.949999999999994 y[1] (closed_form) = 2.546422183735799 y[1] (numeric) = 2.546422183777913 absolute error = 4.211342385929129e-11 relative error = 1.653827245469077e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.999999999999994 y[1] (closed_form) = 2.6236426446749 y[1] (numeric) = 2.623642644717375 absolute error = 4.247446838689939e-11 relative error = 1.618912105774316e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.049999999999994 y[1] (closed_form) = 2.700271372130592 y[1] (numeric) = 2.700271372173409 absolute error = 4.281730525690364e-11 relative error = 1.585666748120932e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.099999999999993 y[1] (closed_form) = 2.776317365982785 y[1] (numeric) = 2.77631736602593 absolute error = 4.314504309377298e-11 relative error = 1.554038584436118e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.149999999999993 y[1] (closed_form) = 2.851789422336615 y[1] (numeric) = 2.851789422380072 absolute error = 4.345768189750743e-11 relative error = 1.523874152738121e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.199999999999993 y[1] (closed_form) = 2.926696139628191 y[1] (numeric) = 2.926696139671948 absolute error = 4.375699802494637e-11 relative error = 1.495098771357429e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.249999999999993 y[1] (closed_form) = 3.001045924503372 y[1] (numeric) = 3.001045924547415 absolute error = 4.404299147608981e-11 relative error = 1.467588053767563e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.299999999999993 y[1] (closed_form) = 3.074846997479596 y[1] (numeric) = 3.074846997523914 absolute error = 4.4317882696987e-11 relative error = 1.44130367245309e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.349999999999993 y[1] (closed_form) = 3.148107398400325 y[1] (numeric) = 3.148107398444905 absolute error = 4.457989533079854e-11 relative error = 1.41608559331398e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.399999999999992 y[1] (closed_form) = 3.220834991691123 y[1] (numeric) = 3.220834991735953 absolute error = 4.482991755594412e-11 relative error = 1.391872532172343e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.449999999999992 y[1] (closed_form) = 3.293037471425993 y[1] (numeric) = 3.293037471471064 absolute error = 4.5070169818473e-11 relative error = 1.368650378550237e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 6.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.499999999999992 y[1] (closed_form) = 3.364722366212119 y[1] (numeric) = 3.364722366257419 absolute error = 4.529976393996549e-11 relative error = 1.346315059894891e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.549999999999992 y[1] (closed_form) = 3.435897043900757 y[1] (numeric) = 3.435897043946278 absolute error = 4.552092036647082e-11 relative error = 1.324862758832585e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.599999999999992 y[1] (closed_form) = 3.506568716131682 y[1] (numeric) = 3.506568716177414 absolute error = 4.57318627411496e-11 relative error = 1.304177001601706e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.649999999999991 y[1] (closed_form) = 3.576744442718148 y[1] (numeric) = 3.576744442764082 absolute error = 4.593392333163138e-11 relative error = 1.284238336489142e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.699999999999991 y[1] (closed_form) = 3.646431135879081 y[1] (numeric) = 3.646431135925209 absolute error = 4.6127546227126e-11 relative error = 1.265005275247179e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.749999999999991 y[1] (closed_form) = 3.71563556432482 y[1] (numeric) = 3.715635564371132 absolute error = 4.631273142763348e-11 relative error = 1.246428252337205e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.799999999999991 y[1] (closed_form) = 3.784364357202438 y[1] (numeric) = 3.784364357248931 absolute error = 4.649258755762276e-11 relative error = 1.228544166714223e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.849999999999991 y[1] (closed_form) = 3.852624007906437 y[1] (numeric) = 3.852624007953101 absolute error = 4.666356190341503e-11 relative error = 1.211215052588861e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.899999999999991 y[1] (closed_form) = 3.920420877760225 y[1] (numeric) = 3.920420877807053 absolute error = 4.682787491105955e-11 relative error = 1.194460400328568e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.94999999999999 y[1] (closed_form) = 3.987761199573665 y[1] (numeric) = 3.987761199620651 absolute error = 4.698597066976617e-11 relative error = 1.178254371771045e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.99999999999999 y[1] (closed_form) = 4.054651081081632 y[1] (numeric) = 4.054651081128769 absolute error = 4.713740509032505e-11 relative error = 1.162551453817094e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.04999999999999 y[1] (closed_form) = 4.121096508268318 y[1] (numeric) = 4.121096508315601 absolute error = 4.728306635115587e-11 relative error = 1.147341884769988e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.09999999999999 y[1] (closed_form) = 4.187103348581837 y[1] (numeric) = 4.187103348629261 absolute error = 4.742428671988819e-11 relative error = 1.132627565449291e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.14999999999999 y[1] (closed_form) = 4.252677354043428 y[1] (numeric) = 4.252677354090986 absolute error = 4.755840166126291e-11 relative error = 1.118316714435074e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.19999999999999 y[1] (closed_form) = 4.317824164255365 y[1] (numeric) = 4.317824164303052 absolute error = 4.768718753211942e-11 relative error = 1.104426343409085e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.249999999999989 y[1] (closed_form) = 4.38254930931154 y[1] (numeric) = 4.382549309359351 absolute error = 4.781064433245774e-11 relative error = 1.090932262436275e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.299999999999989 y[1] (closed_form) = 4.446858212614445 y[1] (numeric) = 4.446858212662375 absolute error = 4.792966024069756e-11 relative error = 1.077831987193453e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.349999999999989 y[1] (closed_form) = 4.510756193602154 y[1] (numeric) = 4.5107561936502 absolute error = 4.804601161367827e-11 relative error = 1.065143172265096e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.399999999999989 y[1] (closed_form) = 4.574248470388741 y[1] (numeric) = 4.574248470436898 absolute error = 4.815703391614079e-11 relative error = 1.052785703004196e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.449999999999989 y[1] (closed_form) = 4.637340162321388 y[1] (numeric) = 4.637340162369652 absolute error = 4.826361532650481e-11 relative error = 1.040760730011764e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 7.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.499999999999988 y[1] (closed_form) = 4.700036292457343 y[1] (numeric) = 4.700036292505708 absolute error = 4.836575584477032e-11 relative error = 1.029050688872086e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.549999999999988 y[1] (closed_form) = 4.762341789963703 y[1] (numeric) = 4.762341790012168 absolute error = 4.846434364935703e-11 relative error = 1.017657820181915e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 8.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.599999999999988 y[1] (closed_form) = 4.824261492442913 y[1] (numeric) = 4.824261492491474 absolute error = 4.856115509710435e-11 relative error = 1.006602879490969e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.05 Radius of convergence (given) for eq 1 = 8.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.649999999999988 y[1] (closed_form) = 4.885800148186696 y[1] (numeric) = 4.885800148235348 absolute error = 4.865263747433346e-11 relative error = 9.957967169899548e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.699999999999988 y[1] (closed_form) = 4.946962418361057 y[1] (numeric) = 4.946962418409798 absolute error = 4.874056713788377e-11 relative error = 9.852625311439431e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.749999999999988 y[1] (closed_form) = 5.007752879124878 y[1] (numeric) = 5.007752879173704 absolute error = 4.882672044459468e-11 relative error = 9.7502256247771e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.799999999999987 y[1] (closed_form) = 5.068176023684505 y[1] (numeric) = 5.068176023733413 absolute error = 4.89075446807874e-11 relative error = 9.649930162692372e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.849999999999987 y[1] (closed_form) = 5.128236264286622 y[1] (numeric) = 5.128236264335611 absolute error = 4.898836891698011e-11 relative error = 9.552673939408441e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.899999999999987 y[1] (closed_form) = 5.187937934151661 y[1] (numeric) = 5.187937934200725 absolute error = 4.906475226107432e-11 relative error = 9.457467086891328e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.949999999999987 y[1] (closed_form) = 5.247285289349807 y[1] (numeric) = 5.247285289398945 absolute error = 4.913758289148973e-11 relative error = 9.364381805430363e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.999999999999987 y[1] (closed_form) = 5.306282510621689 y[1] (numeric) = 5.306282510670899 absolute error = 4.920952534348544e-11 relative error = 9.273823104024667e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.049999999999986 y[1] (closed_form) = 5.36493370514567 y[1] (numeric) = 5.364933705194948 absolute error = 4.927791508180235e-11 relative error = 9.185186209204861e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.099999999999986 y[1] (closed_form) = 5.423242908253601 y[1] (numeric) = 5.423242908302947 absolute error = 4.934541664169956e-11 relative error = 9.098876350642723e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.149999999999986 y[1] (closed_form) = 5.481214085096861 y[1] (numeric) = 5.48121408514627 absolute error = 4.940936548791797e-11 relative error = 9.014310464949634e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.199999999999986 y[1] (closed_form) = 5.538851132264361 y[1] (numeric) = 5.538851132313833 absolute error = 4.947242615571668e-11 relative error = 8.931893090163564e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.249999999999986 y[1] (closed_form) = 5.596157879354212 y[1] (numeric) = 5.596157879403743 absolute error = 4.953104593141688e-11 relative error = 8.850902172390584e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.299999999999986 y[1] (closed_form) = 5.653138090500589 y[1] (numeric) = 5.653138090550178 absolute error = 4.958966570711709e-11 relative error = 8.772059856532869e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.349999999999985 y[1] (closed_form) = 5.709795465857361 y[1] (numeric) = 5.709795465907008 absolute error = 4.96465091259779e-11 relative error = 8.694971548954279e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.399999999999985 y[1] (closed_form) = 5.766133643039922 y[1] (numeric) = 5.766133643089622 absolute error = 4.969979983115991e-11 relative error = 8.619259092468421e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.449999999999985 y[1] (closed_form) = 5.822156198526621 y[1] (numeric) = 5.822156198576372 absolute error = 4.975131417950251e-11 relative error = 8.54516994787821e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 8.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.499999999999985 y[1] (closed_form) = 5.877866649021174 y[1] (numeric) = 5.877866649070977 absolute error = 4.980282852784512e-11 relative error = 8.472942906273428e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.549999999999985 y[1] (closed_form) = 5.933268452777329 y[1] (numeric) = 5.933268452827179 absolute error = 4.985079016250893e-11 relative error = 8.40191044097694e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.599999999999985 y[1] (closed_form) = 5.988365010887024 y[1] (numeric) = 5.988365010936922 absolute error = 4.989875179717274e-11 relative error = 8.33261695077961e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.649999999999984 y[1] (closed_form) = 6.043159668533279 y[1] (numeric) = 6.043159668583224 absolute error = 4.994493707499714e-11 relative error = 8.264705851652462e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.699999999999984 y[1] (closed_form) = 6.097655716208926 y[1] (numeric) = 6.097655716258915 absolute error = 4.998845781756245e-11 relative error = 8.197979706312706e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.749999999999984 y[1] (closed_form) = 6.151856390902318 y[1] (numeric) = 6.15185639095235 absolute error = 5.003197856012775e-11 relative error = 8.132826155389066e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.799999999999984 y[1] (closed_form) = 6.205764877251082 y[1] (numeric) = 6.205764877301156 absolute error = 5.007372294585366e-11 relative error = 8.068904306931206e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.849999999999984 y[1] (closed_form) = 6.259384308664934 y[1] (numeric) = 6.25938430871505 absolute error = 5.011546733157957e-11 relative error = 8.006453168597457e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.899999999999983 y[1] (closed_form) = 6.312717768418561 y[1] (numeric) = 6.312717768468715 absolute error = 5.015365900362667e-11 relative error = 7.944860018063342e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.949999999999983 y[1] (closed_form) = 6.365768290715494 y[1] (numeric) = 6.365768290765684 absolute error = 5.019007431883438e-11 relative error = 7.8843702797095e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.999999999999983 y[1] (closed_form) = 6.418538861723931 y[1] (numeric) = 6.418538861774158 absolute error = 5.022648963404208e-11 relative error = 7.825221707943658e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.049999999999983 y[1] (closed_form) = 6.471032420585368 y[1] (numeric) = 6.47103242063563 absolute error = 5.026201677083009e-11 relative error = 7.767233032388887e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.099999999999984 y[1] (closed_form) = 6.523251860396885 y[1] (numeric) = 6.523251860447181 absolute error = 5.029665572919839e-11 relative error = 7.710365444350369e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.149999999999984 y[1] (closed_form) = 6.575200029167927 y[1] (numeric) = 6.575200029218254 absolute error = 5.03268537954682e-11 relative error = 7.654041485006642e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.199999999999985 y[1] (closed_form) = 6.626879730752352 y[1] (numeric) = 6.626879730802712 absolute error = 5.03606045754168e-11 relative error = 7.599444477876369e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.249999999999986 y[1] (closed_form) = 6.67829372575654 y[1] (numeric) = 6.67829372580693 absolute error = 5.03899144632669e-11 relative error = 7.545327673882532e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.299999999999986 y[1] (closed_form) = 6.729444732424246 y[1] (numeric) = 6.729444732474665 absolute error = 5.041922435111701e-11 relative error = 7.492330549678764e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.349999999999987 y[1] (closed_form) = 6.780335427498959 y[1] (numeric) = 6.780335427549407 absolute error = 5.044853423896711e-11 relative error = 7.44041866046381e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.399999999999988 y[1] (closed_form) = 6.830968447064427 y[1] (numeric) = 6.830968447114903 absolute error = 5.047606776997782e-11 relative error = 7.389298920224063e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.449999999999989 y[1] (closed_form) = 6.881346387363999 y[1] (numeric) = 6.881346387414502 absolute error = 5.050271312256882e-11 relative error = 7.339074401966652e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 9.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.499999999999989 y[1] (closed_form) = 6.931471805599443 y[1] (numeric) = 6.931471805649972 absolute error = 5.052847029674012e-11 relative error = 7.289717352081237e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.54999999999999 y[1] (closed_form) = 6.981347220709834 y[1] (numeric) = 6.981347220760388 absolute error = 5.055422747091143e-11 relative error = 7.241328338596986e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.599999999999991 y[1] (closed_form) = 7.030975114131125 y[1] (numeric) = 7.030975114181704 absolute error = 5.057909646666303e-11 relative error = 7.193752736374677e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.649999999999991 y[1] (closed_form) = 7.080357930536953 y[1] (numeric) = 7.080357930587554 absolute error = 5.060130092715553e-11 relative error = 7.146715098811126e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.699999999999992 y[1] (closed_form) = 7.129498078561242 y[1] (numeric) = 7.129498078611868 absolute error = 5.062616992290714e-11 relative error = 7.100944465521714e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.749999999999993 y[1] (closed_form) = 7.178397931503161 y[1] (numeric) = 7.178397931553809 absolute error = 5.064748620497994e-11 relative error = 7.055541736228925e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.799999999999994 y[1] (closed_form) = 7.227059828014891 y[1] (numeric) = 7.22705982806556 absolute error = 5.066880248705274e-11 relative error = 7.010984230494507e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.849999999999994 y[1] (closed_form) = 7.275486072772772 y[1] (numeric) = 7.275486072823462 absolute error = 5.069011876912555e-11 relative error = 6.967248409535743e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.899999999999995 y[1] (closed_form) = 7.323678937132262 y[1] (numeric) = 7.323678937182972 absolute error = 5.071054687277865e-11 relative error = 6.924190329489705e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.949999999999996 y[1] (closed_form) = 7.371640659767191 y[1] (numeric) = 7.371640659817923 absolute error = 5.073186315485145e-11 relative error = 6.882031490185747e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.999999999999996 y[1] (closed_form) = 7.419373447293768 y[1] (numeric) = 7.41937344734452 absolute error = 5.075140308008486e-11 relative error = 6.840389345625477e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.049999999999997 y[1] (closed_form) = 7.466879474879748 y[1] (numeric) = 7.466879474930518 absolute error = 5.076916664847886e-11 relative error = 6.799248175797893e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.099999999999998 y[1] (closed_form) = 7.51416088683921 y[1] (numeric) = 7.514160886889996 absolute error = 5.078604203845316e-11 relative error = 6.75871102619098e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.149999999999999 y[1] (closed_form) = 7.561219797213337 y[1] (numeric) = 7.56121979726414 absolute error = 5.080380560684716e-11 relative error = 6.718996004529684e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.199999999999999 y[1] (closed_form) = 7.608058290337599 y[1] (numeric) = 7.608058290388422 absolute error = 5.082245735366087e-11 relative error = 6.680082540666979e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.25 y[1] (closed_form) = 7.654678421395714 y[1] (numeric) = 7.654678421446552 absolute error = 5.083755638679577e-11 relative error = 6.641370621749295e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.300000000000001 y[1] (closed_form) = 7.701082216960737 y[1] (numeric) = 7.70108221701159 absolute error = 5.085354359835037e-11 relative error = 6.603428215108698e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.350000000000001 y[1] (closed_form) = 7.747271675523684 y[1] (numeric) = 7.747271675574552 absolute error = 5.086864263148527e-11 relative error = 6.566007332903653e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.400000000000002 y[1] (closed_form) = 7.793248768009979 y[1] (numeric) = 7.793248768060863 absolute error = 5.088374166462017e-11 relative error = 6.529207931035086e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.450000000000003 y[1] (closed_form) = 7.839015438284096 y[1] (numeric) = 7.839015438334997 absolute error = 5.090061705459448e-11 relative error = 6.493241077955608e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 10.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.500000000000004 y[1] (closed_form) = 7.884573603642705 y[1] (numeric) = 7.884573603693619 absolute error = 5.091393973088998e-11 relative error = 6.457411940116525e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.550000000000004 y[1] (closed_form) = 7.929925155296619 y[1] (numeric) = 7.929925155347546 absolute error = 5.092726240718548e-11 relative error = 6.422161799745328e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.600000000000005 y[1] (closed_form) = 7.975071958841886 y[1] (numeric) = 7.975071958892827 absolute error = 5.094147326190068e-11 relative error = 6.387587914541932e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.650000000000006 y[1] (closed_form) = 8.020015854720279 y[1] (numeric) = 8.020015854771234 absolute error = 5.095479593819618e-11 relative error = 6.353453267577534e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.700000000000006 y[1] (closed_form) = 8.06475865866949 y[1] (numeric) = 8.064758658720459 absolute error = 5.096900679291139e-11 relative error = 6.319966777694023e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.750000000000007 y[1] (closed_form) = 8.109302162163294 y[1] (numeric) = 8.109302162214275 absolute error = 5.098144129078719e-11 relative error = 6.286785258620456e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.800000000000008 y[1] (closed_form) = 8.153648132841951 y[1] (numeric) = 8.153648132892945 absolute error = 5.099387578866299e-11 relative error = 6.25411778358028e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.850000000000009 y[1] (closed_form) = 8.197798314933122 y[1] (numeric) = 8.197798314984125 absolute error = 5.100275757285999e-11 relative error = 6.22151895100338e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.900000000000009 y[1] (closed_form) = 8.241754429663503 y[1] (numeric) = 8.241754429714518 absolute error = 5.101519207073579e-11 relative error = 6.189846167597918e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.95000000000001 y[1] (closed_form) = 8.28551817566149 y[1] (numeric) = 8.28551817571252 absolute error = 5.1029402925451e-11 relative error = 6.158866813586702e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.00000000000001 y[1] (closed_form) = 8.329091229351048 y[1] (numeric) = 8.329091229402088 absolute error = 5.10400610664874e-11 relative error = 6.127926764282077e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.05000000000001 y[1] (closed_form) = 8.37247524533703 y[1] (numeric) = 8.372475245388081 absolute error = 5.10507192075238e-11 relative error = 6.097446419558661e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.10000000000001 y[1] (closed_form) = 8.415671856782197 y[1] (numeric) = 8.415671856833256 absolute error = 5.10596009917208e-11 relative error = 6.067204361179058e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.15000000000001 y[1] (closed_form) = 8.458682675776101 y[1] (numeric) = 8.458682675827173 absolute error = 5.10720354895966e-11 relative error = 6.037823789732204e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.20000000000001 y[1] (closed_form) = 8.501509293696111 y[1] (numeric) = 8.501509293747192 absolute error = 5.10809172737936e-11 relative error = 6.008452794572631e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.25000000000001 y[1] (closed_form) = 8.544153281560687 y[1] (numeric) = 8.544153281611777 absolute error = 5.10897990579906e-11 relative error = 5.979504039124456e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.30000000000001 y[1] (closed_form) = 8.586616190375199 y[1] (numeric) = 8.586616190426298 absolute error = 5.10986808421876e-11 relative error = 5.950968310364738e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.35000000000002 y[1] (closed_form) = 8.628899551470411 y[1] (numeric) = 8.628899551521519 absolute error = 5.110756262638461e-11 relative error = 5.922836663184427e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.40000000000002 y[1] (closed_form) = 8.671004876833845 y[1] (numeric) = 8.671004876884963 absolute error = 5.111822076742101e-11 relative error = 5.895305272401883e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.45000000000002 y[1] (closed_form) = 8.712933659434206 y[1] (numeric) = 8.712933659485332 absolute error = 5.112532619477861e-11 relative error = 5.867751114967004e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 11.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.50000000000002 y[1] (closed_form) = 8.754687373539014 y[1] (numeric) = 8.754687373590148 absolute error = 5.113420797897561e-11 relative error = 5.840780578131027e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.55000000000002 y[1] (closed_form) = 8.796267475025651 y[1] (numeric) = 8.796267475076794 absolute error = 5.114308976317261e-11 relative error = 5.814180833902333e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.60000000000002 y[1] (closed_form) = 8.837675401685965 y[1] (numeric) = 8.837675401737117 absolute error = 5.115197154736961e-11 relative error = 5.787944139429622e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.65000000000002 y[1] (closed_form) = 8.878912573524588 y[1] (numeric) = 8.878912573575747 absolute error = 5.115907697472721e-11 relative error = 5.761862902814801e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.70000000000002 y[1] (closed_form) = 8.919980393051121 y[1] (numeric) = 8.919980393102289 absolute error = 5.116795875892421e-11 relative error = 5.736330855478705e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.75000000000002 y[1] (closed_form) = 8.960880245566372 y[1] (numeric) = 8.960880245617549 absolute error = 5.117684054312122e-11 relative error = 5.711139881424292e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.80000000000002 y[1] (closed_form) = 9.001613499442731 y[1] (numeric) = 9.001613499493915 absolute error = 5.118394597047882e-11 relative error = 5.686085719371032e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.85000000000002 y[1] (closed_form) = 9.042181506398878 y[1] (numeric) = 9.042181506450067 absolute error = 5.118927504099702e-11 relative error = 5.661164289256074e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.90000000000002 y[1] (closed_form) = 9.082585601768926 y[1] (numeric) = 9.082585601820124 absolute error = 5.119815682519402e-11 relative error = 5.636958358556253e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 10.95000000000002 y[1] (closed_form) = 9.122827104766181 y[1] (numeric) = 9.122827104817386 absolute error = 5.120526225255162e-11 relative error = 5.612872157338119e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.00000000000002 y[1] (closed_form) = 9.162907318741571 y[1] (numeric) = 9.162907318792781 absolute error = 5.121059132306982e-11 relative error = 5.588902030944373e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.05000000000003 y[1] (closed_form) = 9.202827531436945 y[1] (numeric) = 9.202827531488163 absolute error = 5.121769675042742e-11 relative error = 5.565430469653733e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.10000000000003 y[1] (closed_form) = 9.242589015233341 y[1] (numeric) = 9.242589015284564 absolute error = 5.122302582094562e-11 relative error = 5.542064646228612e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.15000000000003 y[1] (closed_form) = 9.282193027394309 y[1] (numeric) = 9.282193027445539 absolute error = 5.123013124830322e-11 relative error = 5.519184000710715e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.20000000000003 y[1] (closed_form) = 9.321640810304473 y[1] (numeric) = 9.321640810355708 absolute error = 5.123546031882142e-11 relative error = 5.496399331562306e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.25000000000003 y[1] (closed_form) = 9.36093359170337 y[1] (numeric) = 9.360933591754611 absolute error = 5.124078938933962e-11 relative error = 5.473897329509369e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.30000000000003 y[1] (closed_form) = 9.400072584914733 y[1] (numeric) = 9.400072584965979 absolute error = 5.124611845985783e-11 relative error = 5.451672633049425e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.35000000000003 y[1] (closed_form) = 9.439058989071308 y[1] (numeric) = 9.439058989122559 absolute error = 5.125144753037603e-11 relative error = 5.429720016552049e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.40000000000003 y[1] (closed_form) = 9.477893989335284 y[1] (numeric) = 9.477893989386541 absolute error = 5.125677660089423e-11 relative error = 5.408034385969011e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.45000000000003 y[1] (closed_form) = 9.516578757114488 y[1] (numeric) = 9.51657875716575 absolute error = 5.126210567141243e-11 relative error = 5.386610774706137e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 12.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.50000000000003 y[1] (closed_form) = 9.555114450274388 y[1] (numeric) = 9.555114450325656 absolute error = 5.126743474193063e-11 relative error = 5.36544433964979e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.55000000000003 y[1] (closed_form) = 9.593502213346046 y[1] (numeric) = 9.593502213397318 absolute error = 5.127276381244883e-11 relative error = 5.344530357341293e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.60000000000003 y[1] (closed_form) = 9.631743177730081 y[1] (numeric) = 9.631743177781358 absolute error = 5.127631652612763e-11 relative error = 5.323679792946052e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.65000000000003 y[1] (closed_form) = 9.669838461896758 y[1] (numeric) = 9.669838461948039 absolute error = 5.128164559664583e-11 relative error = 5.303257732661941e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.70000000000003 y[1] (closed_form) = 9.707789171582274 y[1] (numeric) = 9.707789171633561 absolute error = 5.128697466716403e-11 relative error = 5.28307462808288e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.75000000000004 y[1] (closed_form) = 9.745596399981334 y[1] (numeric) = 9.745596400032627 absolute error = 5.129230373768223e-11 relative error = 5.263126199006196e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.80000000000004 y[1] (closed_form) = 9.783261227936105 y[1] (numeric) = 9.783261227987399 absolute error = 5.129408009452163e-11 relative error = 5.243045125694014e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.85000000000004 y[1] (closed_form) = 9.820784724121609 y[1] (numeric) = 9.820784724172908 absolute error = 5.129940916503983e-11 relative error = 5.223555001571237e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.90000000000004 y[1] (closed_form) = 9.858167945227681 y[1] (numeric) = 9.858167945278984 absolute error = 5.130296187871863e-11 relative error = 5.204107108314613e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 11.95000000000004 y[1] (closed_form) = 9.895411936137505 y[1] (numeric) = 9.895411936188813 absolute error = 5.130829094923683e-11 relative error = 5.185058619122439e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.00000000000004 y[1] (closed_form) = 9.932517730102862 y[1] (numeric) = 9.932517730154174 absolute error = 5.131184366291563e-11 relative error = 5.166046017456667e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.05000000000004 y[1] (closed_form) = 9.969486348916124 y[1] (numeric) = 9.96948634896744 absolute error = 5.131539637659444e-11 relative error = 5.14724576378736e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.10000000000004 y[1] (closed_form) = 10.00631880307909 y[1] (numeric) = 10.00631880313041 absolute error = 5.131894909027324e-11 relative error = 5.128654213423787e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.15000000000004 y[1] (closed_form) = 10.04301609196872 y[1] (numeric) = 10.04301609202004 absolute error = 5.132250180395204e-11 relative error = 5.110267805404997e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.20000000000004 y[1] (closed_form) = 10.07957920399982 y[1] (numeric) = 10.07957920405115 absolute error = 5.132960723130964e-11 relative error = 5.092435526568493e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.25000000000004 y[1] (closed_form) = 10.11600911678483 y[1] (numeric) = 10.11600911683616 absolute error = 5.132960723130964e-11 relative error = 5.07409657689432e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.30000000000004 y[1] (closed_form) = 10.15230679729062 y[1] (numeric) = 10.15230679734195 absolute error = 5.133493630182784e-11 relative error = 5.056480002705176e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.35000000000004 y[1] (closed_form) = 10.1884732019925 y[1] (numeric) = 10.18847320204384 absolute error = 5.133848901550664e-11 relative error = 5.038879525684639e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.40000000000004 y[1] (closed_form) = 10.22450927702549 y[1] (numeric) = 10.22450927707683 absolute error = 5.134026537234604e-11 relative error = 5.021293832429475e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.45000000000005 y[1] (closed_form) = 10.26041595833277 y[1] (numeric) = 10.26041595838412 absolute error = 5.134559444286424e-11 relative error = 5.00424102213566e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 13.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.50000000000005 y[1] (closed_form) = 10.29619417181161 y[1] (numeric) = 10.29619417186296 absolute error = 5.134914715654304e-11 relative error = 4.987196851543853e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.55000000000005 y[1] (closed_form) = 10.33184483345658 y[1] (numeric) = 10.33184483350793 absolute error = 5.134914715654304e-11 relative error = 4.969988224200216e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.60000000000005 y[1] (closed_form) = 10.36736884950026 y[1] (numeric) = 10.36736884955161 absolute error = 5.135269987022184e-11 relative error = 4.953301133170084e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.65000000000005 y[1] (closed_form) = 10.4027671165515 y[1] (numeric) = 10.40276711660285 absolute error = 5.135625258390064e-11 relative error = 4.93678768432578e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.70000000000005 y[1] (closed_form) = 10.43804052173118 y[1] (numeric) = 10.43804052178254 absolute error = 5.135980529757944e-11 relative error = 4.920445096055372e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.75000000000005 y[1] (closed_form) = 10.47318994280563 y[1] (numeric) = 10.47318994285699 absolute error = 5.136335801125824e-11 relative error = 4.904270646455849e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.80000000000005 y[1] (closed_form) = 10.50821624831765 y[1] (numeric) = 10.50821624836901 absolute error = 5.136335801125824e-11 relative error = 4.887923582604369e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.85000000000005 y[1] (closed_form) = 10.54312029771533 y[1] (numeric) = 10.5431202977667 absolute error = 5.136691072493704e-11 relative error = 4.872078594803487e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.90000000000005 y[1] (closed_form) = 10.57790294147858 y[1] (numeric) = 10.57790294152995 absolute error = 5.136691072493704e-11 relative error = 4.856058049418721e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 12.95000000000005 y[1] (closed_form) = 10.61256502124344 y[1] (numeric) = 10.61256502129482 absolute error = 5.137401615229464e-11 relative error = 4.84086703350773e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.00000000000005 y[1] (closed_form) = 10.64710736992432 y[1] (numeric) = 10.64710736997569 absolute error = 5.137401615229464e-11 relative error = 4.825161836670743e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.05000000000005 y[1] (closed_form) = 10.68153081183405 y[1] (numeric) = 10.68153081188543 absolute error = 5.137756886597344e-11 relative error = 4.809944358261115e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.10000000000005 y[1] (closed_form) = 10.71583616280194 y[1] (numeric) = 10.71583616285332 absolute error = 5.137756886597344e-11 relative error = 4.794545949136591e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.15000000000006 y[1] (closed_form) = 10.7500242302898 y[1] (numeric) = 10.75002423034118 absolute error = 5.137756886597344e-11 relative error = 4.779297959274312e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.20000000000006 y[1] (closed_form) = 10.78409581350594 y[1] (numeric) = 10.78409581355732 absolute error = 5.138112157965224e-11 relative error = 4.764527547622752e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.25000000000006 y[1] (closed_form) = 10.81805170351732 y[1] (numeric) = 10.81805170356871 absolute error = 5.138467429333105e-11 relative error = 4.749900971227945e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.30000000000006 y[1] (closed_form) = 10.85189268335973 y[1] (numeric) = 10.85189268341111 absolute error = 5.138467429333105e-11 relative error = 4.735088688457471e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.35000000000006 y[1] (closed_form) = 10.88561952814612 y[1] (numeric) = 10.88561952819751 absolute error = 5.138645065017045e-11 relative error = 4.7205811775163e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.40000000000006 y[1] (closed_form) = 10.91923300517317 y[1] (numeric) = 10.91923300522456 absolute error = 5.138822700700985e-11 relative error = 4.706212147196036e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.45000000000006 y[1] (closed_form) = 10.95273387402599 y[1] (numeric) = 10.95273387407738 absolute error = 5.139000336384925e-11 relative error = 4.691979550942871e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 14.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.50000000000006 y[1] (closed_form) = 10.98612288668114 y[1] (numeric) = 10.98612288673253 absolute error = 5.139177972068865e-11 relative error = 4.677881382793625e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.55000000000006 y[1] (closed_form) = 11.01940078760789 y[1] (numeric) = 11.01940078765928 absolute error = 5.139177972068865e-11 relative error = 4.663754473699008e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.60000000000006 y[1] (closed_form) = 11.05256831386782 y[1] (numeric) = 11.05256831391922 absolute error = 5.139533243436745e-11 relative error = 4.650080503902514e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.65000000000006 y[1] (closed_form) = 11.08562619521282 y[1] (numeric) = 11.08562619526421 absolute error = 5.139710879120685e-11 relative error = 4.636373975283599e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.70000000000006 y[1] (closed_form) = 11.11857515418134 y[1] (numeric) = 11.11857515423274 absolute error = 5.139710879120685e-11 relative error = 4.62263447235665e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.75000000000006 y[1] (closed_form) = 11.15141590619324 y[1] (numeric) = 11.15141590624464 absolute error = 5.139888514804625e-11 relative error = 4.609180177693889e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.80000000000006 y[1] (closed_form) = 11.18414915964293 y[1] (numeric) = 11.18414915969434 absolute error = 5.140243786172505e-11 relative error = 4.596007897248584e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.85000000000007 y[1] (closed_form) = 11.2167756159911 y[1] (numeric) = 11.2167756160425 absolute error = 5.140066150488565e-11 relative error = 4.582481032392832e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.90000000000007 y[1] (closed_form) = 11.24929596985488 y[1] (numeric) = 11.24929596990628 absolute error = 5.140243786172505e-11 relative error = 4.569391542321397e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 13.95000000000007 y[1] (closed_form) = 11.28171090909658 y[1] (numeric) = 11.28171090914799 absolute error = 5.140599057540385e-11 relative error = 4.556577543035123e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.00000000000007 y[1] (closed_form) = 11.31402111491105 y[1] (numeric) = 11.31402111496246 absolute error = 5.140776693224325e-11 relative error = 4.543722025097831e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.05000000000007 y[1] (closed_form) = 11.34622726191147 y[1] (numeric) = 11.34622726196288 absolute error = 5.140599057540385e-11 relative error = 4.530668158566709e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.10000000000007 y[1] (closed_form) = 11.37833001821395 y[1] (numeric) = 11.37833001826536 absolute error = 5.140954328908265e-11 relative error = 4.518197591983042e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.15000000000007 y[1] (closed_form) = 11.41033004552066 y[1] (numeric) = 11.41033004557207 absolute error = 5.140776693224325e-11 relative error = 4.505370723472132e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.20000000000007 y[1] (closed_form) = 11.44222799920166 y[1] (numeric) = 11.44222799925308 absolute error = 5.141131964592205e-11 relative error = 4.493121413898505e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.25000000000007 y[1] (closed_form) = 11.47402452837546 y[1] (numeric) = 11.47402452842687 absolute error = 5.141131964592205e-11 relative error = 4.480670188457499e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.30000000000007 y[1] (closed_form) = 11.50572027598825 y[1] (numeric) = 11.50572027603967 absolute error = 5.141309600276145e-11 relative error = 4.468481309254275e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.35000000000007 y[1] (closed_form) = 11.53731587889194 y[1] (numeric) = 11.53731587894335 absolute error = 5.141487235960085e-11 relative error = 4.456398082474865e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.40000000000007 y[1] (closed_form) = 11.5688119679209 y[1] (numeric) = 11.56881196797232 absolute error = 5.141487235960085e-11 relative error = 4.444265539293825e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.45000000000007 y[1] (closed_form) = 11.60020916796758 y[1] (numeric) = 11.600209168019 absolute error = 5.141842507327965e-11 relative error = 4.432542924765938e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 15.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.50000000000007 y[1] (closed_form) = 11.63150809805686 y[1] (numeric) = 11.63150809810827 absolute error = 5.141842507327965e-11 relative error = 4.420615507448217e-10 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.55000000000008 y[1] (closed_form) = 11.66270937141929 y[1] (numeric) = 11.66270937147071 absolute error = 5.142020143011905e-11 relative error = 4.40894133537527e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.60000000000008 y[1] (closed_form) = 11.69381359556322 y[1] (numeric) = 11.69381359561464 absolute error = 5.142020143011905e-11 relative error = 4.397214049112988e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.65000000000008 y[1] (closed_form) = 11.7248213723457 y[1] (numeric) = 11.72482137239712 absolute error = 5.142197778695845e-11 relative error = 4.385736562967426e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.70000000000008 y[1] (closed_form) = 11.75573329804243 y[1] (numeric) = 11.75573329809385 absolute error = 5.142375414379785e-11 relative error = 4.374355290312768e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.75000000000008 y[1] (closed_form) = 11.78654996341651 y[1] (numeric) = 11.78654996346793 absolute error = 5.142553050063725e-11 relative error = 4.363068977797027e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.80000000000008 y[1] (closed_form) = 11.81727195378621 y[1] (numeric) = 11.81727195383764 absolute error = 5.142553050063725e-11 relative error = 4.351726075336762e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.85000000000008 y[1] (closed_form) = 11.84789984909167 y[1] (numeric) = 11.8478998491431 absolute error = 5.142553050063725e-11 relative error = 4.340476468880672e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.90000000000008 y[1] (closed_form) = 11.87843422396057 y[1] (numeric) = 11.878434224012 absolute error = 5.142908321431605e-11 relative error = 4.329618049370171e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 14.95000000000008 y[1] (closed_form) = 11.90887564777285 y[1] (numeric) = 11.90887564782428 absolute error = 5.142908321431605e-11 relative error = 4.318550695752214e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.00000000000008 y[1] (closed_form) = 11.93922468472439 y[1] (numeric) = 11.93922468477582 absolute error = 5.143085957115545e-11 relative error = 4.307721893948316e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.05000000000008 y[1] (closed_form) = 11.96948189388976 y[1] (numeric) = 11.96948189394119 absolute error = 5.143085957115545e-11 relative error = 4.296832563605791e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.10000000000008 y[1] (closed_form) = 11.99964782928402 y[1] (numeric) = 11.99964782933545 absolute error = 5.143085957115545e-11 relative error = 4.28603074880608e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.15000000000008 y[1] (closed_form) = 12.02972303992357 y[1] (numeric) = 12.02972303997501 absolute error = 5.143263592799485e-11 relative error = 4.275463014177724e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.20000000000008 y[1] (closed_form) = 12.05970806988614 y[1] (numeric) = 12.05970806993757 absolute error = 5.143263592799485e-11 relative error = 4.264832583835542e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.25000000000009 y[1] (closed_form) = 12.0896034583698 y[1] (numeric) = 12.08960345842124 absolute error = 5.143441228483425e-11 relative error = 4.254433361850714e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.30000000000009 y[1] (closed_form) = 12.11940973975118 y[1] (numeric) = 12.11940973980261 absolute error = 5.143618864167365e-11 relative error = 4.244116648104157e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.35000000000009 y[1] (closed_form) = 12.14912744364275 y[1] (numeric) = 12.14912744369419 absolute error = 5.143618864167365e-11 relative error = 4.233735211049131e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.40000000000009 y[1] (closed_form) = 12.17875709494933 y[1] (numeric) = 12.17875709500076 absolute error = 5.143618864167365e-11 relative error = 4.22343497293372e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.45000000000009 y[1] (closed_form) = 12.20829921392364 y[1] (numeric) = 12.20829921397508 absolute error = 5.143618864167365e-11 relative error = 4.213214940129445e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 16.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.50000000000009 y[1] (closed_form) = 12.23775431622121 y[1] (numeric) = 12.23775431627265 absolute error = 5.143618864167365e-11 relative error = 4.203074135382396e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.55000000000009 y[1] (closed_form) = 12.26712291295431 y[1] (numeric) = 12.26712291300574 absolute error = 5.143796499851305e-11 relative error = 4.193156403788342e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.60000000000009 y[1] (closed_form) = 12.29640551074519 y[1] (numeric) = 12.29640551079663 absolute error = 5.143618864167365e-11 relative error = 4.183026380898567e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.65000000000009 y[1] (closed_form) = 12.32560261177854 y[1] (numeric) = 12.32560261182998 absolute error = 5.143796499851305e-11 relative error = 4.17326167479699e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.70000000000009 y[1] (closed_form) = 12.35471471385312 y[1] (numeric) = 12.35471471390456 absolute error = 5.143796499851305e-11 relative error = 4.1634279859847e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.75000000000009 y[1] (closed_form) = 12.38374231043274 y[1] (numeric) = 12.38374231048418 absolute error = 5.143974135535245e-11 relative error = 4.153812318269642e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.80000000000009 y[1] (closed_form) = 12.41268589069638 y[1] (numeric) = 12.41268589074782 absolute error = 5.143974135535245e-11 relative error = 4.144126566024507e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.85000000000009 y[1] (closed_form) = 12.44154593958773 y[1] (numeric) = 12.44154593963917 absolute error = 5.143796499851305e-11 relative error = 4.134370861007126e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.90000000000009 y[1] (closed_form) = 12.47032293786388 y[1] (numeric) = 12.47032293791532 absolute error = 5.143974135535245e-11 relative error = 4.124972674056818e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 15.9500000000001 y[1] (closed_form) = 12.49901736214341 y[1] (numeric) = 12.49901736219485 absolute error = 5.143974135535245e-11 relative error = 4.115502832338752e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.0000000000001 y[1] (closed_form) = 12.52762968495373 y[1] (numeric) = 12.52762968500518 absolute error = 5.144151771219185e-11 relative error = 4.106245076351156e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.0500000000001 y[1] (closed_form) = 12.5561603747778 y[1] (numeric) = 12.55616037482924 absolute error = 5.143974135535245e-11 relative error = 4.096773202951604e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.1000000000001 y[1] (closed_form) = 12.58460989610011 y[1] (numeric) = 12.58460989615155 absolute error = 5.144151771219185e-11 relative error = 4.087652945693076e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.1500000000001 y[1] (closed_form) = 12.61297870945211 y[1] (numeric) = 12.61297870950355 absolute error = 5.144151771219185e-11 relative error = 4.078459093381472e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.2000000000001 y[1] (closed_form) = 12.64126727145689 y[1] (numeric) = 12.64126727150833 absolute error = 5.144151771219185e-11 relative error = 4.069332338882136e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.2500000000001 y[1] (closed_form) = 12.6694760348733 y[1] (numeric) = 12.66947603492474 absolute error = 5.144329406903125e-11 relative error = 4.060412121813979e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.3000000000001 y[1] (closed_form) = 12.69760544863945 y[1] (numeric) = 12.69760544869089 absolute error = 5.144151771219185e-11 relative error = 4.05127706324375e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.3500000000001 y[1] (closed_form) = 12.72565595791553 y[1] (numeric) = 12.72565595796697 absolute error = 5.144151771219185e-11 relative error = 4.042347041465829e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.4000000000001 y[1] (closed_form) = 12.75362800412615 y[1] (numeric) = 12.75362800417759 absolute error = 5.143974135535245e-11 relative error = 4.033341833297183e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.4500000000001 y[1] (closed_form) = 12.78152202500193 y[1] (numeric) = 12.78152202505337 absolute error = 5.144151771219185e-11 relative error = 4.024678564224755e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 17.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.5000000000001 y[1] (closed_form) = 12.8093384546207 y[1] (numeric) = 12.80933845467214 absolute error = 5.144151771219185e-11 relative error = 4.015938675867793e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.5500000000001 y[1] (closed_form) = 12.83707772344795 y[1] (numeric) = 12.83707772349939 absolute error = 5.143974135535245e-11 relative error = 4.007122373450589e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.6000000000001 y[1] (closed_form) = 12.86474025837686 y[1] (numeric) = 12.8647402584283 absolute error = 5.144151771219185e-11 relative error = 3.998644098445423e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.65000000000011 y[1] (closed_form) = 12.89232648276765 y[1] (numeric) = 12.89232648281909 absolute error = 5.143974135535245e-11 relative error = 3.989950256387678e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.70000000000011 y[1] (closed_form) = 12.91983681648655 y[1] (numeric) = 12.91983681653799 absolute error = 5.144329406903125e-11 relative error = 3.981729397958516e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.75000000000011 y[1] (closed_form) = 12.94727167594406 y[1] (numeric) = 12.9472716759955 absolute error = 5.144329406903125e-11 relative error = 3.973292239214578e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.80000000000011 y[1] (closed_form) = 12.97463147413281 y[1] (numeric) = 12.97463147418425 absolute error = 5.144329406903125e-11 relative error = 3.964913698827781e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.85000000000011 y[1] (closed_form) = 13.00191662066485 y[1] (numeric) = 13.00191662071629 absolute error = 5.144151771219185e-11 relative error = 3.956456514298229e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.90000000000011 y[1] (closed_form) = 13.02912752180846 y[1] (numeric) = 13.0291275218599 absolute error = 5.144329406903125e-11 relative error = 3.948329923314073e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 16.95000000000011 y[1] (closed_form) = 13.05626458052442 y[1] (numeric) = 13.05626458057586 absolute error = 5.144507042587065e-11 relative error = 3.940259490651676e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.00000000000011 y[1] (closed_form) = 13.08332819650185 y[1] (numeric) = 13.08332819655329 absolute error = 5.144507042587065e-11 relative error = 3.932108837537667e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.05000000000011 y[1] (closed_form) = 13.1103187661935 y[1] (numeric) = 13.11031876624494 absolute error = 5.144329406903125e-11 relative error = 3.923878205134406e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.10000000000011 y[1] (closed_form) = 13.13723668285061 y[1] (numeric) = 13.13723668290205 absolute error = 5.144151771219185e-11 relative error = 3.915703047303986e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.15000000000011 y[1] (closed_form) = 13.1640823365573 y[1] (numeric) = 13.16408233660874 absolute error = 5.144151771219185e-11 relative error = 3.907717712258319e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.20000000000011 y[1] (closed_form) = 13.19085611426447 y[1] (numeric) = 13.19085611431591 absolute error = 5.144329406903125e-11 relative error = 3.899920795391056e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.25000000000011 y[1] (closed_form) = 13.21755839982325 y[1] (numeric) = 13.2175583998747 absolute error = 5.144507042587065e-11 relative error = 3.892176517756757e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.30000000000011 y[1] (closed_form) = 13.24418957401809 y[1] (numeric) = 13.24418957406954 absolute error = 5.144507042587065e-11 relative error = 3.88435020039229e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.35000000000012 y[1] (closed_form) = 13.27075001459925 y[1] (numeric) = 13.2707500146507 absolute error = 5.144507042587065e-11 relative error = 3.87657595608956e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.40000000000012 y[1] (closed_form) = 13.29724009631502 y[1] (numeric) = 13.29724009636647 absolute error = 5.144507042587065e-11 relative error = 3.86885323971305e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.45000000000012 y[1] (closed_form) = 13.32366019094341 y[1] (numeric) = 13.32366019099486 absolute error = 5.144507042587065e-11 relative error = 3.861181513833548e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 18.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.50000000000012 y[1] (closed_form) = 13.35001066732346 y[1] (numeric) = 13.35001066737491 absolute error = 5.144507042587065e-11 relative error = 3.853560248591536e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.55000000000012 y[1] (closed_form) = 13.37629189138616 y[1] (numeric) = 13.3762918914376 absolute error = 5.144329406903125e-11 relative error = 3.845856122664223e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.60000000000012 y[1] (closed_form) = 13.4025042261849 y[1] (numeric) = 13.40250422623634 absolute error = 5.144151771219185e-11 relative error = 3.838201939283027e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.65000000000012 y[1] (closed_form) = 13.42864803192561 y[1] (numeric) = 13.42864803197705 absolute error = 5.144329406903125e-11 relative error = 3.830861747714934e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.70000000000012 y[1] (closed_form) = 13.45472366599642 y[1] (numeric) = 13.45472366604786 absolute error = 5.144329406903125e-11 relative error = 3.823437429565486e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.75000000000012 y[1] (closed_form) = 13.48073148299699 y[1] (numeric) = 13.48073148304844 absolute error = 5.144507042587065e-11 relative error = 3.816192800127902e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.80000000000012 y[1] (closed_form) = 13.50667183476746 y[1] (numeric) = 13.5066718348189 absolute error = 5.144329406903125e-11 relative error = 3.808732062077003e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.85000000000012 y[1] (closed_form) = 13.53254507041697 y[1] (numeric) = 13.53254507046841 absolute error = 5.144329406903125e-11 relative error = 3.801450045157409e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.90000000000012 y[1] (closed_form) = 13.55835153635189 y[1] (numeric) = 13.55835153640333 absolute error = 5.144329406903125e-11 relative error = 3.794214505436328e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 17.95000000000012 y[1] (closed_form) = 13.58409157630361 y[1] (numeric) = 13.58409157635506 absolute error = 5.144507042587065e-11 relative error = 3.787155742943648e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.00000000000012 y[1] (closed_form) = 13.60976553135607 y[1] (numeric) = 13.60976553140751 absolute error = 5.144329406903125e-11 relative error = 3.779880994313167e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.05000000000013 y[1] (closed_form) = 13.63537373997281 y[1] (numeric) = 13.63537374002425 absolute error = 5.144507042587065e-11 relative error = 3.772912382669553e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.10000000000013 y[1] (closed_form) = 13.66091653802378 y[1] (numeric) = 13.66091653807522 absolute error = 5.144329406903125e-11 relative error = 3.765727865026045e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.15000000000013 y[1] (closed_form) = 13.68639425881176 y[1] (numeric) = 13.68639425886321 absolute error = 5.144329406903125e-11 relative error = 3.758717825617973e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.20000000000013 y[1] (closed_form) = 13.71180723309849 y[1] (numeric) = 13.71180723314993 absolute error = 5.144151771219185e-11 relative error = 3.751622002679474e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.25000000000013 y[1] (closed_form) = 13.73715578913037 y[1] (numeric) = 13.73715578918181 absolute error = 5.144329406903125e-11 relative error = 3.744828613630207e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.30000000000013 y[1] (closed_form) = 13.76244025266396 y[1] (numeric) = 13.7624402527154 absolute error = 5.144329406903125e-11 relative error = 3.737948585031896e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.35000000000013 y[1] (closed_form) = 13.78766094699106 y[1] (numeric) = 13.7876609470425 absolute error = 5.144151771219185e-11 relative error = 3.730982210105636e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.40000000000013 y[1] (closed_form) = 13.81281819296353 y[1] (numeric) = 13.81281819301497 absolute error = 5.144151771219185e-11 relative error = 3.724186982957394e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.45000000000013 y[1] (closed_form) = 13.83791230901778 y[1] (numeric) = 13.83791230906923 absolute error = 5.144329406903125e-11 relative error = 3.717561791131389e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 19.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.50000000000013 y[1] (closed_form) = 13.86294361119897 y[1] (numeric) = 13.86294361125041 absolute error = 5.144151771219185e-11 relative error = 3.710721124959031e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.55000000000013 y[1] (closed_form) = 13.88791241318484 y[1] (numeric) = 13.88791241323629 absolute error = 5.144151771219185e-11 relative error = 3.704049693124111e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.60000000000013 y[1] (closed_form) = 13.91281902630936 y[1] (numeric) = 13.91281902636081 absolute error = 5.144151771219185e-11 relative error = 3.697418734112412e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.65000000000013 y[1] (closed_form) = 13.93766375958598 y[1] (numeric) = 13.93766375963743 absolute error = 5.144151771219185e-11 relative error = 3.690827860358709e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.70000000000013 y[1] (closed_form) = 13.96244691973065 y[1] (numeric) = 13.9624469197821 absolute error = 5.144507042587065e-11 relative error = 3.684531137101223e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.75000000000014 y[1] (closed_form) = 13.98716881118455 y[1] (numeric) = 13.98716881123599 absolute error = 5.144329406903125e-11 relative error = 3.677891842407429e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.80000000000014 y[1] (closed_form) = 14.01182973613648 y[1] (numeric) = 14.01182973618792 absolute error = 5.144507042587065e-11 relative error = 3.671545500813069e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.85000000000014 y[1] (closed_form) = 14.03642999454511 y[1] (numeric) = 14.03642999459655 absolute error = 5.144151771219185e-11 relative error = 3.664857640595455e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.90000000000014 y[1] (closed_form) = 14.06096988416077 y[1] (numeric) = 14.06096988421221 absolute error = 5.144507042587065e-11 relative error = 3.658714217418378e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 18.95000000000014 y[1] (closed_form) = 14.08544970054717 y[1] (numeric) = 14.08544970059862 absolute error = 5.144684678271005e-11 relative error = 3.652481665580868e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.00000000000014 y[1] (closed_form) = 14.10986973710269 y[1] (numeric) = 14.10986973715413 absolute error = 5.144329406903125e-11 relative error = 3.645908504297403e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.05000000000014 y[1] (closed_form) = 14.1342302850815 y[1] (numeric) = 14.13423028513294 absolute error = 5.144329406903125e-11 relative error = 3.639624728863304e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.10000000000014 y[1] (closed_form) = 14.15853163361442 y[1] (numeric) = 14.15853163366586 absolute error = 5.144151771219185e-11 relative error = 3.633252306338193e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.15000000000014 y[1] (closed_form) = 14.18277406972948 y[1] (numeric) = 14.18277406978092 absolute error = 5.144151771219185e-11 relative error = 3.627042034180344e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.20000000000014 y[1] (closed_form) = 14.2069578783723 y[1] (numeric) = 14.20695787842374 absolute error = 5.144329406903125e-11 relative error = 3.620992932438056e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.25000000000014 y[1] (closed_form) = 14.23108334242614 y[1] (numeric) = 14.23108334247758 absolute error = 5.143974135535245e-11 relative error = 3.614604743547438e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.30000000000014 y[1] (closed_form) = 14.25515074273179 y[1] (numeric) = 14.25515074278323 absolute error = 5.144151771219185e-11 relative error = 3.608626709080584e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.35000000000014 y[1] (closed_form) = 14.27916035810717 y[1] (numeric) = 14.27916035815861 absolute error = 5.144151771219185e-11 relative error = 3.602559003617135e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.40000000000014 y[1] (closed_form) = 14.30311246536672 y[1] (numeric) = 14.30311246541816 absolute error = 5.144151771219185e-11 relative error = 3.596526129312858e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.45000000000014 y[1] (closed_form) = 14.32700733934053 y[1] (numeric) = 14.32700733939197 absolute error = 5.144151771219185e-11 relative error = 3.590527769950852e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 20.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.50000000000015 y[1] (closed_form) = 14.3508452528933 y[1] (numeric) = 14.35084525294474 absolute error = 5.143974135535245e-11 relative error = 3.584439832558406e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.55000000000015 y[1] (closed_form) = 14.37462647694297 y[1] (numeric) = 14.37462647699441 absolute error = 5.143974135535245e-11 relative error = 3.578509774696564e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.60000000000015 y[1] (closed_form) = 14.39835128047928 y[1] (numeric) = 14.39835128053072 absolute error = 5.143974135535245e-11 relative error = 3.572613305045033e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.65000000000015 y[1] (closed_form) = 14.42201993058194 y[1] (numeric) = 14.42201993063338 absolute error = 5.144151771219185e-11 relative error = 3.566873292354142e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.70000000000015 y[1] (closed_form) = 14.44563269243874 y[1] (numeric) = 14.44563269249018 absolute error = 5.143974135535245e-11 relative error = 3.560919929957621e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.75000000000015 y[1] (closed_form) = 14.46918982936332 y[1] (numeric) = 14.46918982941477 absolute error = 5.144151771219185e-11 relative error = 3.555245201621312e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.80000000000015 y[1] (closed_form) = 14.49269160281286 y[1] (numeric) = 14.4926916028643 absolute error = 5.144151771219185e-11 relative error = 3.549479911806559e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.85000000000015 y[1] (closed_form) = 14.5161382724054 y[1] (numeric) = 14.51613827245684 absolute error = 5.144151771219185e-11 relative error = 3.543746742202099e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.90000000000015 y[1] (closed_form) = 14.53953009593713 y[1] (numeric) = 14.53953009598857 absolute error = 5.144151771219185e-11 relative error = 3.53804540949824e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 19.95000000000015 y[1] (closed_form) = 14.56286732939933 y[1] (numeric) = 14.56286732945077 absolute error = 5.144151771219185e-11 relative error = 3.532375633769758e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.00000000000015 y[1] (closed_form) = 14.58615022699524 y[1] (numeric) = 14.58615022704668 absolute error = 5.144151771219185e-11 relative error = 3.526737138425102e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.05000000000015 y[1] (closed_form) = 14.60937904115664 y[1] (numeric) = 14.60937904120808 absolute error = 5.144329406903125e-11 relative error = 3.521251240323658e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.10000000000015 y[1] (closed_form) = 14.63255402256026 y[1] (numeric) = 14.63255402261171 absolute error = 5.144507042587065e-11 relative error = 3.515795694077287e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.15000000000015 y[1] (closed_form) = 14.65567542014406 y[1] (numeric) = 14.6556754201955 absolute error = 5.144329406903125e-11 relative error = 3.510127823813772e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.20000000000016 y[1] (closed_form) = 14.67874348112321 y[1] (numeric) = 14.67874348117465 absolute error = 5.144507042587065e-11 relative error = 3.504732574149059e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.25000000000016 y[1] (closed_form) = 14.701758451006 y[1] (numeric) = 14.70175845105744 absolute error = 5.144329406903125e-11 relative error = 3.499125240049848e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.30000000000016 y[1] (closed_form) = 14.7247205736095 y[1] (numeric) = 14.72472057366095 absolute error = 5.144329406903125e-11 relative error = 3.493668610678487e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.35000000000016 y[1] (closed_form) = 14.74763009107506 y[1] (numeric) = 14.7476300911265 absolute error = 5.144507042587065e-11 relative error = 3.4883618661553e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.40000000000016 y[1] (closed_form) = 14.77048724388362 y[1] (numeric) = 14.77048724393507 absolute error = 5.144329406903125e-11 relative error = 3.482843403851395e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.45000000000016 y[1] (closed_form) = 14.79329227087087 y[1] (numeric) = 14.79329227092232 absolute error = 5.144507042587065e-11 relative error = 3.477594404537653e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 21.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.50000000000016 y[1] (closed_form) = 14.81604540924223 y[1] (numeric) = 14.81604540929367 absolute error = 5.144329406903125e-11 relative error = 3.472133936424155e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.55000000000016 y[1] (closed_form) = 14.83874689458762 y[1] (numeric) = 14.83874689463906 absolute error = 5.144329406903125e-11 relative error = 3.466821992077715e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.60000000000016 y[1] (closed_form) = 14.86139696089614 y[1] (numeric) = 14.86139696094759 absolute error = 5.144507042587065e-11 relative error = 3.46165778097677e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.65000000000016 y[1] (closed_form) = 14.88399584057052 y[1] (numeric) = 14.88399584062196 absolute error = 5.144329406903125e-11 relative error = 3.456282480864989e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.70000000000016 y[1] (closed_form) = 14.90654376444141 y[1] (numeric) = 14.90654376449285 absolute error = 5.144507042587065e-11 relative error = 3.451173607968705e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.75000000000016 y[1] (closed_form) = 14.92904096178156 y[1] (numeric) = 14.92904096183301 absolute error = 5.144329406903125e-11 relative error = 3.445853903189522e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.80000000000016 y[1] (closed_form) = 14.9514876603198 y[1] (numeric) = 14.95148766037125 absolute error = 5.144684678271005e-11 relative error = 3.440918251850375e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.85000000000016 y[1] (closed_form) = 14.97388408625485 y[1] (numeric) = 14.97388408630629 absolute error = 5.144684678271005e-11 relative error = 3.435771673291853e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.90000000000017 y[1] (closed_form) = 14.99623046426901 y[1] (numeric) = 14.99623046432046 absolute error = 5.144507042587065e-11 relative error = 3.430533462955708e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.95000000000017 y[1] (closed_form) = 15.0185270175417 y[1] (numeric) = 15.01852701759315 absolute error = 5.144329406903125e-11 relative error = 3.425322204297749e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.00000000000017 y[1] (closed_form) = 15.04077396776282 y[1] (numeric) = 15.04077396781426 absolute error = 5.144329406903125e-11 relative error = 3.420255778013197e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.05000000000017 y[1] (closed_form) = 15.06297153514594 y[1] (numeric) = 15.06297153519739 absolute error = 5.144329406903125e-11 relative error = 3.41521551368535e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.10000000000017 y[1] (closed_form) = 15.08511993844147 y[1] (numeric) = 15.08511993849292 absolute error = 5.144507042587065e-11 relative error = 3.410318952438222e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.15000000000017 y[1] (closed_form) = 15.1072193949495 y[1] (numeric) = 15.10721939500094 absolute error = 5.144151771219185e-11 relative error = 3.40509503220621e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.20000000000017 y[1] (closed_form) = 15.12927012053264 y[1] (numeric) = 15.12927012058408 absolute error = 5.144329406903125e-11 relative error = 3.400249559905415e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.25000000000017 y[1] (closed_form) = 15.15127232962867 y[1] (numeric) = 15.15127232968011 absolute error = 5.144329406903125e-11 relative error = 3.395311822653514e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.30000000000017 y[1] (closed_form) = 15.17322623526302 y[1] (numeric) = 15.17322623531447 absolute error = 5.144329406903125e-11 relative error = 3.390399198653977e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.35000000000017 y[1] (closed_form) = 15.19513204906121 y[1] (numeric) = 15.19513204911265 absolute error = 5.144507042587065e-11 relative error = 3.385628388076368e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.40000000000017 y[1] (closed_form) = 15.21698998126101 y[1] (numeric) = 15.21698998131246 absolute error = 5.144329406903125e-11 relative error = 3.380648481229283e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.45000000000017 y[1] (closed_form) = 15.23880024072461 y[1] (numeric) = 15.23880024077606 absolute error = 5.144329406903125e-11 relative error = 3.375809988738661e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 22.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.50000000000017 y[1] (closed_form) = 15.26056303495057 y[1] (numeric) = 15.26056303500201 absolute error = 5.144151771219185e-11 relative error = 3.370879409519668e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.55000000000017 y[1] (closed_form) = 15.28227857008565 y[1] (numeric) = 15.28227857013709 absolute error = 5.144151771219185e-11 relative error = 3.366089518410313e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.60000000000018 y[1] (closed_form) = 15.30394705093655 y[1] (numeric) = 15.30394705098799 absolute error = 5.144329406903125e-11 relative error = 3.361439627163575e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.65000000000018 y[1] (closed_form) = 15.3255686809815 y[1] (numeric) = 15.32556868103295 absolute error = 5.144329406903125e-11 relative error = 3.356697238443791e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.70000000000018 y[1] (closed_form) = 15.34714366238171 y[1] (numeric) = 15.34714366243316 absolute error = 5.144329406903125e-11 relative error = 3.351978400718756e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.75000000000018 y[1] (closed_form) = 15.36867219599273 y[1] (numeric) = 15.36867219604417 absolute error = 5.143974135535245e-11 relative error = 3.347051762140193e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.80000000000018 y[1] (closed_form) = 15.39015448137562 y[1] (numeric) = 15.39015448142706 absolute error = 5.144151771219185e-11 relative error = 3.342495215005395e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.85000000000018 y[1] (closed_form) = 15.41159071680813 y[1] (numeric) = 15.41159071685958 absolute error = 5.144151771219185e-11 relative error = 3.33784608334355e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.90000000000018 y[1] (closed_form) = 15.43298109929563 y[1] (numeric) = 15.43298109934707 absolute error = 5.143974135535245e-11 relative error = 3.333104668786265e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.95000000000018 y[1] (closed_form) = 15.45432582458196 y[1] (numeric) = 15.4543258246334 absolute error = 5.144151771219185e-11 relative error = 3.328616097272128e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.00000000000018 y[1] (closed_form) = 15.47562508716021 y[1] (numeric) = 15.47562508721165 absolute error = 5.143974135535245e-11 relative error = 3.323920104398943e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.05000000000018 y[1] (closed_form) = 15.49687908028334 y[1] (numeric) = 15.49687908033478 absolute error = 5.144151771219185e-11 relative error = 3.319475969689976e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.10000000000018 y[1] (closed_form) = 15.51808799597472 y[1] (numeric) = 15.51808799602616 absolute error = 5.144151771219185e-11 relative error = 3.314939168120159e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.15000000000018 y[1] (closed_form) = 15.5392520250385 y[1] (numeric) = 15.53925202508993 absolute error = 5.143974135535245e-11 relative error = 3.310309998992698e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.20000000000018 y[1] (closed_form) = 15.56037135706993 y[1] (numeric) = 15.56037135712137 absolute error = 5.144151771219185e-11 relative error = 3.305931235941818e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.25000000000018 y[1] (closed_form) = 15.58144618046558 y[1] (numeric) = 15.58144618051702 absolute error = 5.144151771219185e-11 relative error = 3.30145976929176e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.30000000000019 y[1] (closed_form) = 15.60247668243336 y[1] (numeric) = 15.60247668248481 absolute error = 5.144151771219185e-11 relative error = 3.297009747824794e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.35000000000019 y[1] (closed_form) = 15.62346304900258 y[1] (numeric) = 15.62346304905402 absolute error = 5.144329406903125e-11 relative error = 3.292694705884395e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.40000000000019 y[1] (closed_form) = 15.64440546503372 y[1] (numeric) = 15.64440546508517 absolute error = 5.144151771219185e-11 relative error = 3.288173387423832e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.45000000000019 y[1] (closed_form) = 15.66530411422832 y[1] (numeric) = 15.66530411427976 absolute error = 5.144151771219185e-11 relative error = 3.28378672620017e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 23.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.50000000000019 y[1] (closed_form) = 15.68615917913853 y[1] (numeric) = 15.68615917918997 absolute error = 5.143974135535245e-11 relative error = 3.27930762195526e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.55000000000019 y[1] (closed_form) = 15.70697084117678 y[1] (numeric) = 15.70697084122822 absolute error = 5.143974135535245e-11 relative error = 3.274962554874047e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.60000000000019 y[1] (closed_form) = 15.72773928062517 y[1] (numeric) = 15.72773928067661 absolute error = 5.143796499851305e-11 relative error = 3.270525031011858e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.65000000000019 y[1] (closed_form) = 15.74846467664489 y[1] (numeric) = 15.74846467669633 absolute error = 5.143796499851305e-11 relative error = 3.266220933574305e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.70000000000019 y[1] (closed_form) = 15.76914720728548 y[1] (numeric) = 15.76914720733692 absolute error = 5.143974135535245e-11 relative error = 3.262049664396998e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.75000000000019 y[1] (closed_form) = 15.789787049494 y[1] (numeric) = 15.78978704954544 absolute error = 5.143974135535245e-11 relative error = 3.257785630300879e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.80000000000019 y[1] (closed_form) = 15.8103843791241 y[1] (numeric) = 15.81038437917554 absolute error = 5.143974135535245e-11 relative error = 3.253541477667871e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.85000000000019 y[1] (closed_form) = 15.83093937094506 y[1] (numeric) = 15.8309393709965 absolute error = 5.143796499851305e-11 relative error = 3.2492048509085e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.90000000000019 y[1] (closed_form) = 15.85145219865064 y[1] (numeric) = 15.85145219870208 absolute error = 5.143796499851305e-11 relative error = 3.245000164899197e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.95000000000019 y[1] (closed_form) = 15.87192303486789 y[1] (numeric) = 15.87192303491932 absolute error = 5.143796499851305e-11 relative error = 3.240814921135435e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.0000000000002 y[1] (closed_form) = 15.89235205116589 y[1] (numeric) = 15.89235205121733 absolute error = 5.143618864167365e-11 relative error = 3.236537202049976e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.0500000000002 y[1] (closed_form) = 15.91273941806437 y[1] (numeric) = 15.91273941811581 absolute error = 5.143618864167365e-11 relative error = 3.232390557673718e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.1000000000002 y[1] (closed_form) = 15.93308530504225 y[1] (numeric) = 15.93308530509368 absolute error = 5.143618864167365e-11 relative error = 3.228262929427482e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.1500000000002 y[1] (closed_form) = 15.95338988054607 y[1] (numeric) = 15.9533898805975 absolute error = 5.143618864167365e-11 relative error = 3.22415417831643e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.2000000000002 y[1] (closed_form) = 15.97365331199839 y[1] (numeric) = 15.97365331204983 absolute error = 5.143796499851305e-11 relative error = 3.220175372147093e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.2500000000002 y[1] (closed_form) = 15.99387576580607 y[1] (numeric) = 15.99387576585751 absolute error = 5.143441228483425e-11 relative error = 3.215881693591611e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.3000000000002 y[1] (closed_form) = 16.01405740736844 y[1] (numeric) = 16.01405740741988 absolute error = 5.143263592799485e-11 relative error = 3.211717968759715e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.3500000000002 y[1] (closed_form) = 16.03419840108545 y[1] (numeric) = 16.03419840113689 absolute error = 5.143618864167365e-11 relative error = 3.207905213284103e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.4000000000002 y[1] (closed_form) = 16.0542989103657 y[1] (numeric) = 16.05429891041713 absolute error = 5.143618864167365e-11 relative error = 3.203888810645173e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.4500000000002 y[1] (closed_form) = 16.07435909763435 y[1] (numeric) = 16.07435909768579 absolute error = 5.143618864167365e-11 relative error = 3.199890479567765e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 24.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.5000000000002 y[1] (closed_form) = 16.09437912434108 y[1] (numeric) = 16.09437912439252 absolute error = 5.143618864167365e-11 relative error = 3.195910090366999e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.5500000000002 y[1] (closed_form) = 16.11435915096781 y[1] (numeric) = 16.11435915101925 absolute error = 5.143618864167365e-11 relative error = 3.191947514622972e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.6000000000002 y[1] (closed_form) = 16.13429933703646 y[1] (numeric) = 16.1342993370879 absolute error = 5.143618864167365e-11 relative error = 3.188002625165217e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.6500000000002 y[1] (closed_form) = 16.15419984111656 y[1] (numeric) = 16.15419984116799 absolute error = 5.143263592799485e-11 relative error = 3.183855370978244e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.70000000000021 y[1] (closed_form) = 16.17406082083285 y[1] (numeric) = 16.17406082088429 absolute error = 5.143618864167365e-11 relative error = 3.180165402582246e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.75000000000021 y[1] (closed_form) = 16.19388243287277 y[1] (numeric) = 16.1938824329242 absolute error = 5.143618864167365e-11 relative error = 3.176272821226662e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.80000000000021 y[1] (closed_form) = 16.21366483299382 y[1] (numeric) = 16.21366483304526 absolute error = 5.143263592799485e-11 relative error = 3.172178311181847e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.85000000000021 y[1] (closed_form) = 16.233408176031 y[1] (numeric) = 16.23340817608243 absolute error = 5.143618864167365e-11 relative error = 3.16853910675519e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.90000000000021 y[1] (closed_form) = 16.25311261590399 y[1] (numeric) = 16.25311261595542 absolute error = 5.143618864167365e-11 relative error = 3.164697732503394e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.95000000000021 y[1] (closed_form) = 16.2727783056244 y[1] (numeric) = 16.27277830567583 absolute error = 5.143618864167365e-11 relative error = 3.160873188071127e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.00000000000021 y[1] (closed_form) = 16.29240539730289 y[1] (numeric) = 16.29240539735432 absolute error = 5.143263592799485e-11 relative error = 3.156847296256772e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.05000000000021 y[1] (closed_form) = 16.31199404215621 y[1] (numeric) = 16.31199404220765 absolute error = 5.143618864167365e-11 relative error = 3.153274118954652e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.10000000000021 y[1] (closed_form) = 16.33154439051425 y[1] (numeric) = 16.33154439056568 absolute error = 5.143618864167365e-11 relative error = 3.149499362200493e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.15000000000021 y[1] (closed_form) = 16.35105659182686 y[1] (numeric) = 16.3510565918783 absolute error = 5.143618864167365e-11 relative error = 3.145740971099337e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.20000000000021 y[1] (closed_form) = 16.37053079467082 y[1] (numeric) = 16.37053079472226 absolute error = 5.143618864167365e-11 relative error = 3.14199883234195e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.25000000000021 y[1] (closed_form) = 16.38996714675653 y[1] (numeric) = 16.38996714680797 absolute error = 5.143263592799485e-11 relative error = 3.138056072197377e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.30000000000021 y[1] (closed_form) = 16.4093657949348 y[1] (numeric) = 16.40936579498623 absolute error = 5.143618864167365e-11 relative error = 3.134562863943886e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.35000000000021 y[1] (closed_form) = 16.42872688520346 y[1] (numeric) = 16.4287268852549 absolute error = 5.143618864167365e-11 relative error = 3.130868812969292e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.40000000000022 y[1] (closed_form) = 16.448050562714 y[1] (numeric) = 16.44805056276543 absolute error = 5.143263592799485e-11 relative error = 3.126974575612457e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.45000000000022 y[1] (closed_form) = 16.46733697177805 y[1] (numeric) = 16.46733697182949 absolute error = 5.143618864167365e-11 relative error = 3.123528031874595e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 25.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.50000000000022 y[1] (closed_form) = 16.4865862558739 y[1] (numeric) = 16.48658625592533 absolute error = 5.142908321431605e-11 relative error = 3.119450104232021e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.55000000000022 y[1] (closed_form) = 16.50579855765284 y[1] (numeric) = 16.50579855770427 absolute error = 5.143263592799485e-11 relative error = 3.116034389269118e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.60000000000022 y[1] (closed_form) = 16.52497401894556 y[1] (numeric) = 16.52497401899699 absolute error = 5.143263592799485e-11 relative error = 3.112418565319882e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.65000000000022 y[1] (closed_form) = 16.5441127807684 y[1] (numeric) = 16.54411278081983 absolute error = 5.143263592799485e-11 relative error = 3.108818019409442e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.70000000000022 y[1] (closed_form) = 16.56321498332959 y[1] (numeric) = 16.56321498338102 absolute error = 5.143263592799485e-11 relative error = 3.105232648357239e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.75000000000022 y[1] (closed_form) = 16.58228076603541 y[1] (numeric) = 16.58228076608684 absolute error = 5.142908321431605e-11 relative error = 3.101448102341595e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.80000000000022 y[1] (closed_form) = 16.60131026749627 y[1] (numeric) = 16.6013102675477 absolute error = 5.142908321431605e-11 relative error = 3.097893020830357e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.85000000000022 y[1] (closed_form) = 16.6203036255328 y[1] (numeric) = 16.62030362558422 absolute error = 5.142908321431605e-11 relative error = 3.094352809253651e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.90000000000022 y[1] (closed_form) = 16.63926097718178 y[1] (numeric) = 16.63926097723322 absolute error = 5.143263592799485e-11 relative error = 3.091040882075646e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.95000000000022 y[1] (closed_form) = 16.65818245870216 y[1] (numeric) = 16.6581824587536 absolute error = 5.143263592799485e-11 relative error = 3.087529870410722e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.00000000000022 y[1] (closed_form) = 16.67706820558085 y[1] (numeric) = 16.67706820563228 absolute error = 5.142908321431605e-11 relative error = 3.083820404182656e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.05000000000022 y[1] (closed_form) = 16.69591835253856 y[1] (numeric) = 16.69591835258999 absolute error = 5.143263592799485e-11 relative error = 3.080551476233992e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.10000000000023 y[1] (closed_form) = 16.71473303353562 y[1] (numeric) = 16.71473303358705 absolute error = 5.143263592799485e-11 relative error = 3.0770839010592e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.15000000000023 y[1] (closed_form) = 16.73351238177762 y[1] (numeric) = 16.73351238182905 absolute error = 5.143263592799485e-11 relative error = 3.073630613498916e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.20000000000023 y[1] (closed_form) = 16.75225652972112 y[1] (numeric) = 16.75225652977256 absolute error = 5.143618864167365e-11 relative error = 3.070403593117012e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.25000000000023 y[1] (closed_form) = 16.77096560907924 y[1] (numeric) = 16.77096560913067 absolute error = 5.143618864167365e-11 relative error = 3.066978362523612e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.30000000000023 y[1] (closed_form) = 16.78963975082719 y[1] (numeric) = 16.78963975087863 absolute error = 5.143618864167365e-11 relative error = 3.063567140512321e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.35000000000023 y[1] (closed_form) = 16.80827908520782 y[1] (numeric) = 16.80827908525925 absolute error = 5.143263592799485e-11 relative error = 3.059958468517952e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.40000000000023 y[1] (closed_form) = 16.82688374173701 y[1] (numeric) = 16.82688374178845 absolute error = 5.143974135535245e-11 relative error = 3.056997489544811e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.45000000000023 y[1] (closed_form) = 16.84545384920914 y[1] (numeric) = 16.84545384926058 absolute error = 5.143618864167365e-11 relative error = 3.053416613295252e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 26.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.50000000000023 y[1] (closed_form) = 16.86398953570237 y[1] (numeric) = 16.86398953575381 absolute error = 5.143618864167365e-11 relative error = 3.050060516983793e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.55000000000023 y[1] (closed_form) = 16.88249092858399 y[1] (numeric) = 16.88249092863542 absolute error = 5.143618864167365e-11 relative error = 3.046717978955718e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.60000000000023 y[1] (closed_form) = 16.90095815451564 y[1] (numeric) = 16.90095815456707 absolute error = 5.143618864167365e-11 relative error = 3.043388911529304e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.65000000000023 y[1] (closed_form) = 16.91939133945853 y[1] (numeric) = 16.91939133950996 absolute error = 5.143618864167365e-11 relative error = 3.040073227794953e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.70000000000023 y[1] (closed_form) = 16.9377906086786 y[1] (numeric) = 16.93779060873004 absolute error = 5.143974135535245e-11 relative error = 3.036980592320921e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.75000000000023 y[1] (closed_form) = 16.95615608675162 y[1] (numeric) = 16.95615608680305 absolute error = 5.143618864167365e-11 relative error = 3.033481667573371e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.80000000000024 y[1] (closed_form) = 16.97448789756822 y[1] (numeric) = 16.97448789761966 absolute error = 5.143618864167365e-11 relative error = 3.030205621051015e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.85000000000024 y[1] (closed_form) = 16.99278616433899 y[1] (numeric) = 16.99278616439042 absolute error = 5.143263592799485e-11 relative error = 3.026733546258072e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.90000000000024 y[1] (closed_form) = 17.01105100959933 y[1] (numeric) = 17.01105100965076 absolute error = 5.143618864167365e-11 relative error = 3.023692575646751e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.95000000000024 y[1] (closed_form) = 17.02928255521448 y[1] (numeric) = 17.02928255526592 absolute error = 5.143618864167365e-11 relative error = 3.020455411136716e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.00000000000024 y[1] (closed_form) = 17.04748092238434 y[1] (numeric) = 17.04748092243577 absolute error = 5.143618864167365e-11 relative error = 3.017231042865397e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.05000000000024 y[1] (closed_form) = 17.06564623164832 y[1] (numeric) = 17.06564623169975 absolute error = 5.143618864167365e-11 relative error = 3.014019389801074e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.10000000000024 y[1] (closed_form) = 17.08377860289013 y[1] (numeric) = 17.08377860294156 absolute error = 5.143263592799485e-11 relative error = 3.010612413303799e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.15000000000024 y[1] (closed_form) = 17.10187815534252 y[1] (numeric) = 17.10187815539395 absolute error = 5.143263592799485e-11 relative error = 3.007426170436585e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.20000000000024 y[1] (closed_form) = 17.11994500759201 y[1] (numeric) = 17.11994500764344 absolute error = 5.143618864167365e-11 relative error = 3.004459921971932e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.25000000000024 y[1] (closed_form) = 17.13797927758352 y[1] (numeric) = 17.13797927763495 absolute error = 5.143263592799485e-11 relative error = 3.001091032667355e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.30000000000024 y[1] (closed_form) = 17.155981082625 y[1] (numeric) = 17.15598108267643 absolute error = 5.143263592799485e-11 relative error = 2.997941981883164e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.35000000000024 y[1] (closed_form) = 17.17395053939202 y[1] (numeric) = 17.17395053944345 absolute error = 5.142908321431605e-11 relative error = 2.994598307264993e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.40000000000024 y[1] (closed_form) = 17.19188776393228 y[1] (numeric) = 17.19188776398371 absolute error = 5.143263592799485e-11 relative error = 2.991680531785343e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.45000000000024 y[1] (closed_form) = 17.20979287167016 y[1] (numeric) = 17.2097928717216 absolute error = 5.143263592799485e-11 relative error = 2.98856798053976e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.50000000000025 y[1] (closed_form) = 17.22766597741112 y[1] (numeric) = 17.22766597746255 absolute error = 5.142908321431605e-11 relative error = 2.985261223531368e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.55000000000025 y[1] (closed_form) = 17.24550719534614 y[1] (numeric) = 17.24550719539757 absolute error = 5.143263592799485e-11 relative error = 2.982378850642006e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.60000000000025 y[1] (closed_form) = 17.26331663905609 y[1] (numeric) = 17.26331663910752 absolute error = 5.142908321431605e-11 relative error = 2.979096328336133e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.65000000000025 y[1] (closed_form) = 17.28109442151608 y[1] (numeric) = 17.28109442156751 absolute error = 5.142908321431605e-11 relative error = 2.976031607713659e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.70000000000025 y[1] (closed_form) = 17.29884065509976 y[1] (numeric) = 17.2988406551512 absolute error = 5.143263592799485e-11 relative error = 2.973183981137621e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.75000000000025 y[1] (closed_form) = 17.31655545158358 y[1] (numeric) = 17.31655545163501 absolute error = 5.143263592799485e-11 relative error = 2.970142420748659e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.80000000000025 y[1] (closed_form) = 17.33423892215101 y[1] (numeric) = 17.33423892220243 absolute error = 5.142908321431605e-11 relative error = 2.966907485542735e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.85000000000025 y[1] (closed_form) = 17.35189117739669 y[1] (numeric) = 17.35189117744813 absolute error = 5.143263592799485e-11 relative error = 2.964093965445863e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.90000000000025 y[1] (closed_form) = 17.36951232733069 y[1] (numeric) = 17.36951232738212 absolute error = 5.143263592799485e-11 relative error = 2.961086929715713e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.95000000000025 y[1] (closed_form) = 17.38710248138248 y[1] (numeric) = 17.38710248143392 absolute error = 5.143263592799485e-11 relative error = 2.958091262363419e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.00000000000025 y[1] (closed_form) = 17.40466174840514 y[1] (numeric) = 17.40466174845657 absolute error = 5.142908321431605e-11 relative error = 2.954902770174704e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.05000000000025 y[1] (closed_form) = 17.42219023667928 y[1] (numeric) = 17.42219023673071 absolute error = 5.143263592799485e-11 relative error = 2.952133757540583e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.10000000000025 y[1] (closed_form) = 17.43968805391716 y[1] (numeric) = 17.43968805396859 absolute error = 5.143263592799485e-11 relative error = 2.949171783863559e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.15000000000025 y[1] (closed_form) = 17.45715530726657 y[1] (numeric) = 17.457155307318 absolute error = 5.143263592799485e-11 relative error = 2.946220906139612e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.20000000000026 y[1] (closed_form) = 17.47459210331484 y[1] (numeric) = 17.47459210336627 absolute error = 5.143263592799485e-11 relative error = 2.94328105765847e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.25000000000026 y[1] (closed_form) = 17.49199854809268 y[1] (numeric) = 17.49199854814411 absolute error = 5.143263592799485e-11 relative error = 2.940352172256671e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.30000000000026 y[1] (closed_form) = 17.50937474707809 y[1] (numeric) = 17.50937474712952 absolute error = 5.143263592799485e-11 relative error = 2.937434184311909e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.35000000000026 y[1] (closed_form) = 17.52672080520017 y[1] (numeric) = 17.5267208052516 absolute error = 5.143263592799485e-11 relative error = 2.934527028737447e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.40000000000026 y[1] (closed_form) = 17.54403682684295 y[1] (numeric) = 17.54403682689438 absolute error = 5.142908321431605e-11 relative error = 2.931428138342019e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.45000000000026 y[1] (closed_form) = 17.56132291584913 y[1] (numeric) = 17.56132291590056 absolute error = 5.143263592799485e-11 relative error = 2.928744956997334e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 28.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.50000000000026 y[1] (closed_form) = 17.57857917552383 y[1] (numeric) = 17.57857917557526 absolute error = 5.142908321431605e-11 relative error = 2.92566780857495e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.55000000000026 y[1] (closed_form) = 17.59580570863829 y[1] (numeric) = 17.59580570868972 absolute error = 5.143263592799485e-11 relative error = 2.923005446846068e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.60000000000026 y[1] (closed_form) = 17.61300261743355 y[1] (numeric) = 17.61300261748499 absolute error = 5.143263592799485e-11 relative error = 2.92015149518494e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.65000000000026 y[1] (closed_form) = 17.6301700036241 y[1] (numeric) = 17.63017000367553 absolute error = 5.143618864167365e-11 relative error = 2.917509509613368e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.70000000000026 y[1] (closed_form) = 17.64730796840145 y[1] (numeric) = 17.64730796845288 absolute error = 5.143618864167365e-11 relative error = 2.914676206352448e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.75000000000026 y[1] (closed_form) = 17.66441661243774 y[1] (numeric) = 17.66441661248918 absolute error = 5.143618864167365e-11 relative error = 2.911853234114552e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.80000000000026 y[1] (closed_form) = 17.6814960358893 y[1] (numeric) = 17.68149603594074 absolute error = 5.143618864167365e-11 relative error = 2.909040532388787e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.85000000000026 y[1] (closed_form) = 17.69854633840014 y[1] (numeric) = 17.69854633845158 absolute error = 5.143618864167365e-11 relative error = 2.90623804114769e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.90000000000027 y[1] (closed_form) = 17.71556761910545 y[1] (numeric) = 17.71556761915688 absolute error = 5.143618864167365e-11 relative error = 2.90344570084235e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.95000000000027 y[1] (closed_form) = 17.73255997663504 y[1] (numeric) = 17.73255997668648 absolute error = 5.143974135535245e-11 relative error = 2.900863802131842e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.00000000000027 y[1] (closed_form) = 17.74952350911683 y[1] (numeric) = 17.74952350916827 absolute error = 5.143618864167365e-11 relative error = 2.897891237207245e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.05000000000027 y[1] (closed_form) = 17.76645831418016 y[1] (numeric) = 17.7664583142316 absolute error = 5.143618864167365e-11 relative error = 2.895128997129397e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.10000000000027 y[1] (closed_form) = 17.78336448895924 y[1] (numeric) = 17.78336448901067 absolute error = 5.143263592799485e-11 relative error = 2.892176897117904e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.15000000000027 y[1] (closed_form) = 17.80024213009643 y[1] (numeric) = 17.80024213014787 absolute error = 5.143618864167365e-11 relative error = 2.88963421203726e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.20000000000027 y[1] (closed_form) = 17.81709133374563 y[1] (numeric) = 17.81709133379706 absolute error = 5.143618864167365e-11 relative error = 2.886901553019114e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.25000000000027 y[1] (closed_form) = 17.83391219557548 y[1] (numeric) = 17.83391219562691 absolute error = 5.143618864167365e-11 relative error = 2.884178641096751e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.30000000000027 y[1] (closed_form) = 17.85070481077268 y[1] (numeric) = 17.85070481082411 absolute error = 5.143618864167365e-11 relative error = 2.881465420381192e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.35000000000027 y[1] (closed_form) = 17.8674692740452 y[1] (numeric) = 17.86746927409663 absolute error = 5.143618864167365e-11 relative error = 2.878761835420718e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.40000000000027 y[1] (closed_form) = 17.8842056796255 y[1] (numeric) = 17.88420567967693 absolute error = 5.143618864167365e-11 relative error = 2.876067831196557e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.45000000000027 y[1] (closed_form) = 17.90091412127367 y[1] (numeric) = 17.90091412132511 absolute error = 5.143974135535245e-11 relative error = 2.873581818607845e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 29.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.50000000000027 y[1] (closed_form) = 17.91759469228064 y[1] (numeric) = 17.91759469233208 absolute error = 5.143263592799485e-11 relative error = 2.870510066295525e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.55000000000027 y[1] (closed_form) = 17.93424748547125 y[1] (numeric) = 17.93424748552269 absolute error = 5.143618864167365e-11 relative error = 2.868042759159129e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.60000000000027 y[1] (closed_form) = 17.95087259320739 y[1] (numeric) = 17.95087259325883 absolute error = 5.143618864167365e-11 relative error = 2.865386536203099e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.65000000000028 y[1] (closed_form) = 17.96747010739103 y[1] (numeric) = 17.96747010744247 absolute error = 5.143618864167365e-11 relative error = 2.862739625236112e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.70000000000028 y[1] (closed_form) = 17.98404011946733 y[1] (numeric) = 17.98404011951876 absolute error = 5.143618864167365e-11 relative error = 2.860101973749219e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.75000000000028 y[1] (closed_form) = 18.00058272042759 y[1] (numeric) = 18.00058272047903 absolute error = 5.143263592799485e-11 relative error = 2.857276163044854e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.80000000000028 y[1] (closed_form) = 18.01709800081232 y[1] (numeric) = 18.01709800086376 absolute error = 5.143618864167365e-11 relative error = 2.85485424119659e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.85000000000028 y[1] (closed_form) = 18.03358605071416 y[1] (numeric) = 18.0335860507656 absolute error = 5.143618864167365e-11 relative error = 2.852244057117896e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.90000000000028 y[1] (closed_form) = 18.05004695978085 y[1] (numeric) = 18.05004695983228 absolute error = 5.143618864167365e-11 relative error = 2.849642926485669e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.95000000000028 y[1] (closed_form) = 18.06648081721815 y[1] (numeric) = 18.06648081726958 absolute error = 5.143263592799485e-11 relative error = 2.846854152081311e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.00000000000028 y[1] (closed_form) = 18.08288771179275 y[1] (numeric) = 18.08288771184418 absolute error = 5.143263592799485e-11 relative error = 2.844271155566214e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.05000000000028 y[1] (closed_form) = 18.09926773183513 y[1] (numeric) = 18.09926773188656 absolute error = 5.143263592799485e-11 relative error = 2.841697061452329e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.10000000000028 y[1] (closed_form) = 18.11562096524244 y[1] (numeric) = 18.11562096529387 absolute error = 5.142908321431605e-11 relative error = 2.838935707088955e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.15000000000028 y[1] (closed_form) = 18.13194749948129 y[1] (numeric) = 18.13194749953272 absolute error = 5.143263592799485e-11 relative error = 2.836575383282254e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.20000000000028 y[1] (closed_form) = 18.1482474215906 y[1] (numeric) = 18.14824742164204 absolute error = 5.143263592799485e-11 relative error = 2.834027701584368e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.25000000000028 y[1] (closed_form) = 18.16452081818436 y[1] (numeric) = 18.16452081823579 absolute error = 5.143263592799485e-11 relative error = 2.831488726997194e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.30000000000028 y[1] (closed_form) = 18.18076777545438 y[1] (numeric) = 18.18076777550581 absolute error = 5.143263592799485e-11 relative error = 2.828958411615235e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.35000000000029 y[1] (closed_form) = 18.19698837917306 y[1] (numeric) = 18.19698837922449 absolute error = 5.143263592799485e-11 relative error = 2.826436707892878e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.40000000000029 y[1] (closed_form) = 18.21318271469609 y[1] (numeric) = 18.21318271474752 absolute error = 5.142908321431605e-11 relative error = 2.823728505881528e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.45000000000029 y[1] (closed_form) = 18.22935086696514 y[1] (numeric) = 18.22935086701657 absolute error = 5.143263592799485e-11 relative error = 2.821418947023508e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 30.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.50000000000029 y[1] (closed_form) = 18.24549292051055 y[1] (numeric) = 18.24549292056198 absolute error = 5.142908321431605e-11 relative error = 2.818728079223466e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.55000000000029 y[1] (closed_form) = 18.26160895945397 y[1] (numeric) = 18.2616089595054 absolute error = 5.143263592799485e-11 relative error = 2.81643507109314e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.60000000000029 y[1] (closed_form) = 18.27769906751098 y[1] (numeric) = 18.27769906756241 absolute error = 5.142908321431605e-11 relative error = 2.813761350614006e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.65000000000029 y[1] (closed_form) = 18.29376332799371 y[1] (numeric) = 18.29376332804514 absolute error = 5.143263592799485e-11 relative error = 2.811484712349534e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.70000000000029 y[1] (closed_form) = 18.30980182381346 y[1] (numeric) = 18.30980182386489 absolute error = 5.143263592799485e-11 relative error = 2.809021988490467e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.75000000000029 y[1] (closed_form) = 18.32581463748319 y[1] (numeric) = 18.32581463753463 absolute error = 5.143263592799485e-11 relative error = 2.8065675084804e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.80000000000029 y[1] (closed_form) = 18.34180185112017 y[1] (numeric) = 18.3418018511716 absolute error = 5.142908321431605e-11 relative error = 2.803927532952559e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.85000000000029 y[1] (closed_form) = 18.35776354644839 y[1] (numeric) = 18.35776354649982 absolute error = 5.143263592799485e-11 relative error = 2.80168310251198e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.90000000000029 y[1] (closed_form) = 18.37369980480117 y[1] (numeric) = 18.3736998048526 absolute error = 5.143263592799485e-11 relative error = 2.799253088621551e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.95000000000029 y[1] (closed_form) = 18.38961070712358 y[1] (numeric) = 18.38961070717502 absolute error = 5.143263592799485e-11 relative error = 2.79683114270991e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.00000000000029 y[1] (closed_form) = 18.40549633397497 y[1] (numeric) = 18.4054963340264 absolute error = 5.142908321431605e-11 relative error = 2.794224197006976e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.0500000000003 y[1] (closed_form) = 18.42135676553131 y[1] (numeric) = 18.42135676558274 absolute error = 5.143263592799485e-11 relative error = 2.792011282482288e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.1000000000003 y[1] (closed_form) = 18.43719208158775 y[1] (numeric) = 18.43719208163919 absolute error = 5.143263592799485e-11 relative error = 2.789613282781704e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.1500000000003 y[1] (closed_form) = 18.45300236156094 y[1] (numeric) = 18.45300236161237 absolute error = 5.143263592799485e-11 relative error = 2.78722318028491e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.2000000000003 y[1] (closed_form) = 18.46878768449144 y[1] (numeric) = 18.46878768454287 absolute error = 5.143263592799485e-11 relative error = 2.784840933072382e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.2500000000003 y[1] (closed_form) = 18.4845481290461 y[1] (numeric) = 18.48454812909753 absolute error = 5.143263592799485e-11 relative error = 2.782466499528601e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.3000000000003 y[1] (closed_form) = 18.5002837735204 y[1] (numeric) = 18.50028377357183 absolute error = 5.143263592799485e-11 relative error = 2.780099838339279e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.3500000000003 y[1] (closed_form) = 18.51599469584081 y[1] (numeric) = 18.51599469589225 absolute error = 5.143263592799485e-11 relative error = 2.777740908488594e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.4000000000003 y[1] (closed_form) = 18.53168097356708 y[1] (numeric) = 18.53168097361851 absolute error = 5.142908321431605e-11 relative error = 2.775197958980226e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.4500000000003 y[1] (closed_form) = 18.54734268389453 y[1] (numeric) = 18.54734268394596 absolute error = 5.143263592799485e-11 relative error = 2.773046080215904e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 31.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.5000000000003 y[1] (closed_form) = 18.56297990365636 y[1] (numeric) = 18.56297990370779 absolute error = 5.143263592799485e-11 relative error = 2.770710101230253e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.5500000000003 y[1] (closed_form) = 18.57859270932588 y[1] (numeric) = 18.57859270937731 absolute error = 5.143263592799485e-11 relative error = 2.768381692450648e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.6000000000003 y[1] (closed_form) = 18.59418117701879 y[1] (numeric) = 18.59418117707023 absolute error = 5.143263592799485e-11 relative error = 2.766060814313365e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.6500000000003 y[1] (closed_form) = 18.60974538249538 y[1] (numeric) = 18.60974538254681 absolute error = 5.143263592799485e-11 relative error = 2.763747427537252e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.7000000000003 y[1] (closed_form) = 18.62528540116272 y[1] (numeric) = 18.62528540121415 absolute error = 5.143263592799485e-11 relative error = 2.761441493121178e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.75000000000031 y[1] (closed_form) = 18.64080130807691 y[1] (numeric) = 18.64080130812834 absolute error = 5.143263592799485e-11 relative error = 2.759142972341512e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.80000000000031 y[1] (closed_form) = 18.6562931779452 y[1] (numeric) = 18.65629317799663 absolute error = 5.142908321431605e-11 relative error = 2.756661396976419e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.85000000000031 y[1] (closed_form) = 18.67176108512819 y[1] (numeric) = 18.67176108517962 absolute error = 5.143263592799485e-11 relative error = 2.754568018169442e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.90000000000031 y[1] (closed_form) = 18.68720510364193 y[1] (numeric) = 18.68720510369336 absolute error = 5.142908321431605e-11 relative error = 2.752101393926109e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 30.95000000000031 y[1] (closed_form) = 18.70262530716008 y[1] (numeric) = 18.70262530721151 absolute error = 5.143263592799485e-11 relative error = 2.750022260687887e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.00000000000031 y[1] (closed_form) = 18.71802176901601 y[1] (numeric) = 18.71802176906744 absolute error = 5.143263592799485e-11 relative error = 2.747760236775204e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.05000000000031 y[1] (closed_form) = 18.73339456220488 y[1] (numeric) = 18.7333945622563 absolute error = 5.142908321431605e-11 relative error = 2.745315753829026e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.10000000000031 y[1] (closed_form) = 18.74874375938571 y[1] (numeric) = 18.74874375943714 absolute error = 5.142908321431605e-11 relative error = 2.743068222294649e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.15000000000031 y[1] (closed_form) = 18.76406943288349 y[1] (numeric) = 18.76406943293492 absolute error = 5.142908321431605e-11 relative error = 2.740827803812539e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.20000000000031 y[1] (closed_form) = 18.77937165469117 y[1] (numeric) = 18.7793716547426 absolute error = 5.142908321431605e-11 relative error = 2.738594462050004e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.25000000000031 y[1] (closed_form) = 18.7946504964717 y[1] (numeric) = 18.79465049652313 absolute error = 5.142908321431605e-11 relative error = 2.736368160928067e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.30000000000031 y[1] (closed_form) = 18.80990602956007 y[1] (numeric) = 18.8099060296115 absolute error = 5.142908321431605e-11 relative error = 2.734148864619229e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.35000000000031 y[1] (closed_form) = 18.82513832496529 y[1] (numeric) = 18.82513832501672 absolute error = 5.142908321431605e-11 relative error = 2.73193653754525e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.40000000000031 y[1] (closed_form) = 18.84034745337236 y[1] (numeric) = 18.84034745342378 absolute error = 5.142553050063725e-11 relative error = 2.729542574939734e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.45000000000032 y[1] (closed_form) = 18.85553348514425 y[1] (numeric) = 18.85553348519568 absolute error = 5.142908321431605e-11 relative error = 2.727532650022106e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 32.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.50000000000032 y[1] (closed_form) = 18.87069649032389 y[1] (numeric) = 18.87069649037532 absolute error = 5.142908321431605e-11 relative error = 2.725341019643167e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.55000000000032 y[1] (closed_form) = 18.88583653863605 y[1] (numeric) = 18.88583653868747 absolute error = 5.142908321431605e-11 relative error = 2.723156218635275e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.60000000000032 y[1] (closed_form) = 18.90095369948926 y[1] (numeric) = 18.90095369954069 absolute error = 5.142908321431605e-11 relative error = 2.720978212634093e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.65000000000032 y[1] (closed_form) = 18.91604804197781 y[1] (numeric) = 18.91604804202924 absolute error = 5.142553050063725e-11 relative error = 2.718619152717078e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.70000000000032 y[1] (closed_form) = 18.93111963488352 y[1] (numeric) = 18.93111963493495 absolute error = 5.142908321431605e-11 relative error = 2.716642449374732e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.75000000000032 y[1] (closed_form) = 18.94616854667773 y[1] (numeric) = 18.94616854672915 absolute error = 5.142553050063725e-11 relative error = 2.714297108354126e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.80000000000032 y[1] (closed_form) = 18.96119484552307 y[1] (numeric) = 18.9611948455745 absolute error = 5.142553050063725e-11 relative error = 2.712146092036986e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.85000000000032 y[1] (closed_form) = 18.97619859927542 y[1] (numeric) = 18.97619859932685 absolute error = 5.142553050063725e-11 relative error = 2.710001701953144e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.90000000000032 y[1] (closed_form) = 18.99117987548564 y[1] (numeric) = 18.99117987553707 absolute error = 5.142908321431605e-11 relative error = 2.70805097690124e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 31.95000000000032 y[1] (closed_form) = 19.00613874140146 y[1] (numeric) = 19.00613874145289 absolute error = 5.142908321431605e-11 relative error = 2.705919593351542e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.00000000000032 y[1] (closed_form) = 19.0210752639693 y[1] (numeric) = 19.02107526402073 absolute error = 5.142553050063725e-11 relative error = 2.703607960484239e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.05000000000032 y[1] (closed_form) = 19.035989509836 y[1] (numeric) = 19.03598950988743 absolute error = 5.142553050063725e-11 relative error = 2.701489747830834e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.10000000000031 y[1] (closed_form) = 19.05088154535068 y[1] (numeric) = 19.0508815454021 absolute error = 5.142553050063725e-11 relative error = 2.699377998767072e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.15000000000031 y[1] (closed_form) = 19.06575143656646 y[1] (numeric) = 19.06575143661788 absolute error = 5.142553050063725e-11 relative error = 2.697272681422225e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.20000000000031 y[1] (closed_form) = 19.08059924924225 y[1] (numeric) = 19.08059924929368 absolute error = 5.142908321431605e-11 relative error = 2.69535995921923e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.25000000000031 y[1] (closed_form) = 19.09542504884448 y[1] (numeric) = 19.0954250488959 absolute error = 5.142908321431605e-11 relative error = 2.693267265995118e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.3000000000003 y[1] (closed_form) = 19.11022890054882 y[1] (numeric) = 19.11022890060025 absolute error = 5.142908321431605e-11 relative error = 2.691180910598046e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.3500000000003 y[1] (closed_form) = 19.12501086924193 y[1] (numeric) = 19.12501086929336 absolute error = 5.142908321431605e-11 relative error = 2.68910086200409e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.4000000000003 y[1] (closed_form) = 19.13977101952313 y[1] (numeric) = 19.13977101957456 absolute error = 5.142908321431605e-11 relative error = 2.687027089397092e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.45000000000029 y[1] (closed_form) = 19.15450941570613 y[1] (numeric) = 19.15450941575757 absolute error = 5.143263592799485e-11 relative error = 2.68514503878766e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 33.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.50000000000029 y[1] (closed_form) = 19.1692261218207 y[1] (numeric) = 19.16922612187213 absolute error = 5.143263592799485e-11 relative error = 2.683083584133222e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.55000000000029 y[1] (closed_form) = 19.1839212016143 y[1] (numeric) = 19.18392120166573 absolute error = 5.143263592799485e-11 relative error = 2.681028314673586e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.60000000000029 y[1] (closed_form) = 19.19859471855379 y[1] (numeric) = 19.19859471860523 absolute error = 5.143263592799485e-11 relative error = 2.678979200404164e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.65000000000028 y[1] (closed_form) = 19.21324673582707 y[1] (numeric) = 19.2132467358785 absolute error = 5.143263592799485e-11 relative error = 2.676936211519528e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.70000000000028 y[1] (closed_form) = 19.22787731634467 y[1] (numeric) = 19.22787731639611 absolute error = 5.143263592799485e-11 relative error = 2.674899318411736e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.75000000000028 y[1] (closed_form) = 19.24248652274142 y[1] (numeric) = 19.24248652279286 absolute error = 5.143618864167365e-11 relative error = 2.673053120285917e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.80000000000027 y[1] (closed_form) = 19.25707441737802 y[1] (numeric) = 19.25707441742945 absolute error = 5.143263592799485e-11 relative error = 2.670843702072464e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.85000000000027 y[1] (closed_form) = 19.27164106234266 y[1] (numeric) = 19.2716410623941 absolute error = 5.143618864167365e-11 relative error = 2.669009269904961e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.90000000000027 y[1] (closed_form) = 19.2861865194526 y[1] (numeric) = 19.28618651950404 absolute error = 5.143618864167365e-11 relative error = 2.666996328682896e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 32.95000000000027 y[1] (closed_form) = 19.30071085025575 y[1] (numeric) = 19.30071085030719 absolute error = 5.143974135535245e-11 relative error = 2.665173410163328e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.00000000000026 y[1] (closed_form) = 19.31521411603221 y[1] (numeric) = 19.31521411608365 absolute error = 5.143974135535245e-11 relative error = 2.663172204374163e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.05000000000026 y[1] (closed_form) = 19.32969637779586 y[1] (numeric) = 19.3296963778473 absolute error = 5.143974135535245e-11 relative error = 2.661176893313316e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.10000000000026 y[1] (closed_form) = 19.34415769629586 y[1] (numeric) = 19.3441576963473 absolute error = 5.144329406903125e-11 relative error = 2.659371107116334e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.15000000000025 y[1] (closed_form) = 19.35859813201819 y[1] (numeric) = 19.35859813206963 absolute error = 5.144329406903125e-11 relative error = 2.657387364426276e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.20000000000025 y[1] (closed_form) = 19.37301774518721 y[1] (numeric) = 19.37301774523864 absolute error = 5.143974135535245e-11 relative error = 2.655226048514384e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.25000000000025 y[1] (closed_form) = 19.38741659576708 y[1] (numeric) = 19.38741659581852 absolute error = 5.144329406903125e-11 relative error = 2.653437285721866e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.30000000000025 y[1] (closed_form) = 19.40179474346336 y[1] (numeric) = 19.4017947435148 absolute error = 5.143974135535245e-11 relative error = 2.651287782161647e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.35000000000024 y[1] (closed_form) = 19.41615224772439 y[1] (numeric) = 19.41615224777584 absolute error = 5.144329406903125e-11 relative error = 2.649510233164787e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.40000000000024 y[1] (closed_form) = 19.43048916774288 y[1] (numeric) = 19.43048916779432 absolute error = 5.144329406903125e-11 relative error = 2.647555273823665e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.45000000000024 y[1] (closed_form) = 19.44480556245726 y[1] (numeric) = 19.4448055625087 absolute error = 5.144329406903125e-11 relative error = 2.645605989928465e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 34.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.50000000000023 y[1] (closed_form) = 19.4591014905532 y[1] (numeric) = 19.45910149060465 absolute error = 5.144329406903125e-11 relative error = 2.643662354811469e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.55000000000023 y[1] (closed_form) = 19.47337701046505 y[1] (numeric) = 19.4733770105165 absolute error = 5.144684678271005e-11 relative error = 2.641906781502888e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.60000000000023 y[1] (closed_form) = 19.48763218037726 y[1] (numeric) = 19.48763218042871 absolute error = 5.144684678271005e-11 relative error = 2.639974231169735e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.65000000000023 y[1] (closed_form) = 19.5018670582258 y[1] (numeric) = 19.50186705827725 absolute error = 5.145039949638885e-11 relative error = 2.638229424022625e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.70000000000022 y[1] (closed_form) = 19.51608170169957 y[1] (numeric) = 19.51608170175102 absolute error = 5.145039949638885e-11 relative error = 2.63630785537797e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.75000000000022 y[1] (closed_form) = 19.53027616824184 y[1] (numeric) = 19.53027616829329 absolute error = 5.145039949638885e-11 relative error = 2.634391805480575e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.80000000000022 y[1] (closed_form) = 19.54445051505157 y[1] (numeric) = 19.54445051510302 absolute error = 5.145395221006765e-11 relative error = 2.632663024751806e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.85000000000021 y[1] (closed_form) = 19.55860479908488 y[1] (numeric) = 19.55860479913633 absolute error = 5.145395221006765e-11 relative error = 2.630757803975625e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.90000000000021 y[1] (closed_form) = 19.57273907705634 y[1] (numeric) = 19.5727390771078 absolute error = 5.145395221006765e-11 relative error = 2.628858025823441e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 33.95000000000021 y[1] (closed_form) = 19.58685340544042 y[1] (numeric) = 19.58685340549188 absolute error = 5.145395221006765e-11 relative error = 2.626963665117127e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.00000000000021 y[1] (closed_form) = 19.60094784047276 y[1] (numeric) = 19.60094784052421 absolute error = 5.145750492374646e-11 relative error = 2.625255948974831e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.0500000000002 y[1] (closed_form) = 19.61502243815155 y[1] (numeric) = 19.61502243820301 absolute error = 5.145750492374646e-11 relative error = 2.62337221820663e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.1000000000002 y[1] (closed_form) = 19.6290772542389 y[1] (numeric) = 19.62907725429036 absolute error = 5.145750492374646e-11 relative error = 2.621493830670731e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.1500000000002 y[1] (closed_form) = 19.6431123442621 y[1] (numeric) = 19.64311234431356 absolute error = 5.146105763742526e-11 relative error = 2.619801624891557e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.20000000000019 y[1] (closed_form) = 19.65712776351499 y[1] (numeric) = 19.65712776356645 absolute error = 5.146105763742526e-11 relative error = 2.617933721372082e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.25000000000019 y[1] (closed_form) = 19.67112356705922 y[1] (numeric) = 19.67112356711068 absolute error = 5.146461035110406e-11 relative error = 2.616251693791678e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.30000000000019 y[1] (closed_form) = 19.6850998097256 y[1] (numeric) = 19.68509980977706 absolute error = 5.146461035110406e-11 relative error = 2.614394178772592e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.35000000000019 y[1] (closed_form) = 19.69905654611534 y[1] (numeric) = 19.69905654616681 absolute error = 5.146816306478286e-11 relative error = 2.612722235925171e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.40000000000018 y[1] (closed_form) = 19.71299383060138 y[1] (numeric) = 19.71299383065285 absolute error = 5.146461035110406e-11 relative error = 2.610694793157861e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.45000000000018 y[1] (closed_form) = 19.7269117173296 y[1] (numeric) = 19.72691171738107 absolute error = 5.146816306478286e-11 relative error = 2.609032969898139e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 35.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.50000000000018 y[1] (closed_form) = 19.74081026022014 y[1] (numeric) = 19.74081026027162 absolute error = 5.147171577846166e-11 relative error = 2.60737604485175e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.55000000000017 y[1] (closed_form) = 19.75468951296862 y[1] (numeric) = 19.7546895130201 absolute error = 5.147171577846166e-11 relative error = 2.605544154195455e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.60000000000017 y[1] (closed_form) = 19.7685495290474 y[1] (numeric) = 19.76854952909887 absolute error = 5.147171577846166e-11 relative error = 2.603717369492913e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.65000000000017 y[1] (closed_form) = 19.78239036170678 y[1] (numeric) = 19.78239036175825 absolute error = 5.147171577846166e-11 relative error = 2.6018956676791e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.70000000000017 y[1] (closed_form) = 19.7962120639763 y[1] (numeric) = 19.79621206402777 absolute error = 5.147526849214046e-11 relative error = 2.6002584901488e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.75000000000016 y[1] (closed_form) = 19.81001468866588 y[1] (numeric) = 19.81001468871736 absolute error = 5.147526849214046e-11 relative error = 2.598446760445441e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.80000000000016 y[1] (closed_form) = 19.82379828836709 y[1] (numeric) = 19.82379828841857 absolute error = 5.147882120581926e-11 relative error = 2.596819260213509e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.85000000000016 y[1] (closed_form) = 19.83756291545432 y[1] (numeric) = 19.8375629155058 absolute error = 5.147882120581926e-11 relative error = 2.595017413440187e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.90000000000015 y[1] (closed_form) = 19.85130862208599 y[1] (numeric) = 19.85130862213747 absolute error = 5.148237391949806e-11 relative error = 2.593399503255935e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 34.95000000000015 y[1] (closed_form) = 19.86503546020571 y[1] (numeric) = 19.86503546025719 absolute error = 5.148237391949806e-11 relative error = 2.591607451324677e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.00000000000015 y[1] (closed_form) = 19.87874348154349 y[1] (numeric) = 19.87874348159498 absolute error = 5.148592663317686e-11 relative error = 2.589999045009016e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.05000000000015 y[1] (closed_form) = 19.89243273761691 y[1] (numeric) = 19.8924327376684 absolute error = 5.148592663317686e-11 relative error = 2.588216700907383e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.10000000000014 y[1] (closed_form) = 19.90610327973224 y[1] (numeric) = 19.90610327978373 absolute error = 5.148592663317686e-11 relative error = 2.586439239748052e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.15000000000014 y[1] (closed_form) = 19.91975515898564 y[1] (numeric) = 19.91975515903713 absolute error = 5.148947934685566e-11 relative error = 2.584844991110706e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.20000000000014 y[1] (closed_form) = 19.93338842626428 y[1] (numeric) = 19.93338842631577 absolute error = 5.148947934685566e-11 relative error = 2.583077108908037e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.25000000000014 y[1] (closed_form) = 19.94700313224749 y[1] (numeric) = 19.94700313229898 absolute error = 5.149303206053446e-11 relative error = 2.581492152938394e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.30000000000013 y[1] (closed_form) = 19.96059932740789 y[1] (numeric) = 19.96059932745938 absolute error = 5.148947934685566e-11 relative error = 2.579555778976811e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.35000000000013 y[1] (closed_form) = 19.97417706201249 y[1] (numeric) = 19.97417706206398 absolute error = 5.149303206053446e-11 relative error = 2.577980154109353e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.40000000000013 y[1] (closed_form) = 19.98773638612385 y[1] (numeric) = 19.98773638617534 absolute error = 5.149303206053446e-11 relative error = 2.576231298321637e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.45000000000012 y[1] (closed_form) = 20.00127734960114 y[1] (numeric) = 20.00127734965263 absolute error = 5.149658477421326e-11 relative error = 2.574664801357809e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 36.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.50000000000012 y[1] (closed_form) = 20.01480000210127 y[1] (numeric) = 20.01480000215277 absolute error = 5.149303206053446e-11 relative error = 2.572747769407059e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.55000000000012 y[1] (closed_form) = 20.02830439307999 y[1] (numeric) = 20.02830439313148 absolute error = 5.149303206053446e-11 relative error = 2.571013054820851e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.60000000000012 y[1] (closed_form) = 20.04179057179292 y[1] (numeric) = 20.04179057184442 absolute error = 5.149303206053446e-11 relative error = 2.569283012716759e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.65000000000011 y[1] (closed_form) = 20.05525858729671 y[1] (numeric) = 20.0552585873482 absolute error = 5.149303206053446e-11 relative error = 2.567557622675127e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.70000000000011 y[1] (closed_form) = 20.06870848845004 y[1] (numeric) = 20.06870848850153 absolute error = 5.149303206053446e-11 relative error = 2.565836864398613e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.75000000000011 y[1] (closed_form) = 20.08214032391471 y[1] (numeric) = 20.0821403239662 absolute error = 5.149303206053446e-11 relative error = 2.564120717711262e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.8000000000001 y[1] (closed_form) = 20.09555414215672 y[1] (numeric) = 20.09555414220822 absolute error = 5.149658477421326e-11 relative error = 2.562585953585775e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.8500000000001 y[1] (closed_form) = 20.10894999144729 y[1] (numeric) = 20.10894999149878 absolute error = 5.149658477421326e-11 relative error = 2.56087885225811e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.9000000000001 y[1] (closed_form) = 20.12232791986388 y[1] (numeric) = 20.12232791991538 absolute error = 5.149658477421326e-11 relative error = 2.559176303024964e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 35.9500000000001 y[1] (closed_form) = 20.1356879752913 y[1] (numeric) = 20.1356879753428 absolute error = 5.150013748789206e-11 relative error = 2.55765472483922e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.00000000000009 y[1] (closed_form) = 20.14903020542267 y[1] (numeric) = 20.14903020547417 absolute error = 5.150013748789206e-11 relative error = 2.55596110397571e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.05000000000009 y[1] (closed_form) = 20.16235465776046 y[1] (numeric) = 20.16235465781196 absolute error = 5.150369020157086e-11 relative error = 2.554448182060282e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.10000000000009 y[1] (closed_form) = 20.17566137961751 y[1] (numeric) = 20.17566137966901 absolute error = 5.150369020157086e-11 relative error = 2.552763412930916e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.15000000000008 y[1] (closed_form) = 20.18895041811804 y[1] (numeric) = 20.18895041816955 absolute error = 5.150724291524966e-11 relative error = 2.551259072340177e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.20000000000008 y[1] (closed_form) = 20.20222182019867 y[1] (numeric) = 20.20222182025018 absolute error = 5.151079562892846e-11 relative error = 2.549758936783217e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.25000000000008 y[1] (closed_form) = 20.21547563260935 y[1] (numeric) = 20.21547563266086 absolute error = 5.151079562892846e-11 relative error = 2.548087245883891e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.30000000000008 y[1] (closed_form) = 20.22871190191444 y[1] (numeric) = 20.22871190196594 absolute error = 5.150724291524966e-11 relative error = 2.546244326628382e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.35000000000007 y[1] (closed_form) = 20.2419306744936 y[1] (numeric) = 20.2419306745451 absolute error = 5.150724291524966e-11 relative error = 2.54458152947598e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.40000000000007 y[1] (closed_form) = 20.25513199654282 y[1] (numeric) = 20.25513199659433 absolute error = 5.151079562892846e-11 relative error = 2.543098491667219e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.45000000000007 y[1] (closed_form) = 20.2683159140754 y[1] (numeric) = 20.26831591412692 absolute error = 5.151434834260726e-11 relative error = 2.541619568246069e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 37.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.50000000000006 y[1] (closed_form) = 20.28148247292287 y[1] (numeric) = 20.28148247297439 absolute error = 5.151790105628606e-11 relative error = 2.540144741641342e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.55000000000006 y[1] (closed_form) = 20.29463171873596 y[1] (numeric) = 20.29463171878747 absolute error = 5.151434834260726e-11 relative error = 2.538323880745731e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.60000000000006 y[1] (closed_form) = 20.30776369698557 y[1] (numeric) = 20.30776369703708 absolute error = 5.151079562892846e-11 relative error = 2.53650753463192e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.65000000000006 y[1] (closed_form) = 20.32087845296367 y[1] (numeric) = 20.32087845301519 absolute error = 5.151434834260726e-11 relative error = 2.535045345694404e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.70000000000005 y[1] (closed_form) = 20.33397603178431 y[1] (numeric) = 20.33397603183582 absolute error = 5.151434834260726e-11 relative error = 2.53341246503313e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.75000000000005 y[1] (closed_form) = 20.34705647838446 y[1] (numeric) = 20.34705647843597 absolute error = 5.151434834260726e-11 relative error = 2.531783818329356e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.80000000000005 y[1] (closed_form) = 20.36011983752501 y[1] (numeric) = 20.36011983757653 absolute error = 5.151790105628606e-11 relative error = 2.530333881499816e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.85000000000004 y[1] (closed_form) = 20.37316615379166 y[1] (numeric) = 20.37316615384318 absolute error = 5.152145376996486e-11 relative error = 2.528887919582209e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.90000000000004 y[1] (closed_form) = 20.38619547159582 y[1] (numeric) = 20.38619547164734 absolute error = 5.152145376996486e-11 relative error = 2.527271645253767e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 36.95000000000004 y[1] (closed_form) = 20.39920783517553 y[1] (numeric) = 20.39920783522706 absolute error = 5.152500648364366e-11 relative error = 2.525833694129834e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.00000000000004 y[1] (closed_form) = 20.41220328859639 y[1] (numeric) = 20.41220328864792 absolute error = 5.152500648364366e-11 relative error = 2.524225619114275e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.05000000000003 y[1] (closed_form) = 20.42518187575239 y[1] (numeric) = 20.42518187580391 absolute error = 5.152145376996486e-11 relative error = 2.52244773551457e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.10000000000003 y[1] (closed_form) = 20.43814364036685 y[1] (numeric) = 20.43814364041838 absolute error = 5.152855919732247e-11 relative error = 2.521195667474894e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.15000000000003 y[1] (closed_form) = 20.45108862599331 y[1] (numeric) = 20.45108862604484 absolute error = 5.152500648364366e-11 relative error = 2.519426101266582e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.20000000000002 y[1] (closed_form) = 20.46401687601637 y[1] (numeric) = 20.46401687606789 absolute error = 5.152500648364366e-11 relative error = 2.517834440609287e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.25000000000002 y[1] (closed_form) = 20.47692843365256 y[1] (numeric) = 20.47692843370409 absolute error = 5.152500648364366e-11 relative error = 2.516246840955185e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.30000000000002 y[1] (closed_form) = 20.48982334195128 y[1] (numeric) = 20.48982334200281 absolute error = 5.152855919732247e-11 relative error = 2.514836674644327e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.35000000000002 y[1] (closed_form) = 20.50270164379556 y[1] (numeric) = 20.50270164384709 absolute error = 5.152855919732247e-11 relative error = 2.513257037660488e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.40000000000001 y[1] (closed_form) = 20.51556338190301 y[1] (numeric) = 20.51556338195454 absolute error = 5.152855919732247e-11 relative error = 2.511681411721617e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.45000000000001 y[1] (closed_form) = 20.52840859882657 y[1] (numeric) = 20.5284085988781 absolute error = 5.152855919732247e-11 relative error = 2.510109780271418e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 38.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.50000000000001 y[1] (closed_form) = 20.54123733695546 y[1] (numeric) = 20.54123733700699 absolute error = 5.153211191100127e-11 relative error = 2.508715082040873e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.55 y[1] (closed_form) = 20.55404963851595 y[1] (numeric) = 20.55404963856748 absolute error = 5.153211191100127e-11 relative error = 2.507151282462409e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.6 y[1] (closed_form) = 20.5668455455722 y[1] (numeric) = 20.56684554562373 absolute error = 5.153211191100127e-11 relative error = 2.505591428535599e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.65 y[1] (closed_form) = 20.57962510002712 y[1] (numeric) = 20.57962510007865 absolute error = 5.153211191100127e-11 relative error = 2.504035504074045e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.7 y[1] (closed_form) = 20.59238834362316 y[1] (numeric) = 20.5923883436747 absolute error = 5.153566462468007e-11 relative error = 2.502656018559357e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.74999999999999 y[1] (closed_form) = 20.60513531794317 y[1] (numeric) = 20.6051353179947 absolute error = 5.153566462468007e-11 relative error = 2.501107798103236e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.79999999999999 y[1] (closed_form) = 20.61786606441115 y[1] (numeric) = 20.61786606446269 absolute error = 5.153921733835887e-11 relative error = 2.499735771749997e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.84999999999999 y[1] (closed_form) = 20.63058062429311 y[1] (numeric) = 20.63058062434465 absolute error = 5.153921733835887e-11 relative error = 2.498195192706788e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.89999999999998 y[1] (closed_form) = 20.64327903869788 y[1] (numeric) = 20.64327903874941 absolute error = 5.153566462468007e-11 relative error = 2.496486363821917e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.94999999999998 y[1] (closed_form) = 20.65596134857783 y[1] (numeric) = 20.65596134862936 absolute error = 5.153921733835887e-11 relative error = 2.495125570222243e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 37.99999999999998 y[1] (closed_form) = 20.66862759472975 y[1] (numeric) = 20.6686275947813 absolute error = 5.154277005203767e-11 relative error = 2.49376838475625e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.04999999999998 y[1] (closed_form) = 20.68127781779562 y[1] (numeric) = 20.68127781784716 absolute error = 5.154277005203767e-11 relative error = 2.492243008683276e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.09999999999997 y[1] (closed_form) = 20.69391205826334 y[1] (numeric) = 20.69391205831488 absolute error = 5.154632276571647e-11 relative error = 2.49089310037603e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.14999999999997 y[1] (closed_form) = 20.70653035646756 y[1] (numeric) = 20.7065303565191 absolute error = 5.154277005203767e-11 relative error = 2.489203607012731e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.19999999999997 y[1] (closed_form) = 20.71913275259043 y[1] (numeric) = 20.71913275264198 absolute error = 5.154632276571647e-11 relative error = 2.487861021078299e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.24999999999996 y[1] (closed_form) = 20.7317192866624 y[1] (numeric) = 20.73171928671394 absolute error = 5.154277005203767e-11 relative error = 2.486179237686155e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.29999999999996 y[1] (closed_form) = 20.74428999856291 y[1] (numeric) = 20.74428999861445 absolute error = 5.154277005203767e-11 relative error = 2.484672652359197e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.34999999999996 y[1] (closed_form) = 20.75684492802122 y[1] (numeric) = 20.75684492807277 absolute error = 5.154987547939527e-11 relative error = 2.483512097245773e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.39999999999996 y[1] (closed_form) = 20.76938411461716 y[1] (numeric) = 20.76938411466871 absolute error = 5.154632276571647e-11 relative error = 2.481841660843423e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.44999999999995 y[1] (closed_form) = 20.78190759778182 y[1] (numeric) = 20.78190759783337 absolute error = 5.155342819307407e-11 relative error = 2.480687971039612e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 39.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.49999999999995 y[1] (closed_form) = 20.79441541679835 y[1] (numeric) = 20.7944154168499 absolute error = 5.154987547939527e-11 relative error = 2.479024990418906e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.54999999999995 y[1] (closed_form) = 20.80690761080266 y[1] (numeric) = 20.80690761085422 absolute error = 5.155342819307407e-11 relative error = 2.477707363217599e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.59999999999994 y[1] (closed_form) = 20.81938421878422 y[1] (numeric) = 20.81938421883577 absolute error = 5.155698090675287e-11 relative error = 2.476393171140757e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.64999999999994 y[1] (closed_form) = 20.83184527958669 y[1] (numeric) = 20.83184527963824 absolute error = 5.155698090675287e-11 relative error = 2.474911858013559e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.69999999999994 y[1] (closed_form) = 20.84429083190873 y[1] (numeric) = 20.84429083196029 absolute error = 5.155698090675287e-11 relative error = 2.473434156264444e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.74999999999994 y[1] (closed_form) = 20.85672091430471 y[1] (numeric) = 20.85672091435626 absolute error = 5.155342819307407e-11 relative error = 2.471789712529348e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.79999999999993 y[1] (closed_form) = 20.86913556518535 y[1] (numeric) = 20.86913556523691 absolute error = 5.155698090675287e-11 relative error = 2.470489529655559e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.84999999999993 y[1] (closed_form) = 20.88153482281855 y[1] (numeric) = 20.88153482287012 absolute error = 5.156053362043167e-11 relative error = 2.469192712984309e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.89999999999993 y[1] (closed_form) = 20.89391872533002 y[1] (numeric) = 20.89391872538158 absolute error = 5.155698090675287e-11 relative error = 2.467559177601736e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.94999999999992 y[1] (closed_form) = 20.90628731070399 y[1] (numeric) = 20.90628731075554 absolute error = 5.155698090675287e-11 relative error = 2.466099319335183e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 38.99999999999992 y[1] (closed_form) = 20.91864061678391 y[1] (numeric) = 20.91864061683547 absolute error = 5.155698090675287e-11 relative error = 2.464642987622557e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.04999999999992 y[1] (closed_form) = 20.9309786812732 y[1] (numeric) = 20.93097868132476 absolute error = 5.156053362043167e-11 relative error = 2.463359903307461e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.09999999999992 y[1] (closed_form) = 20.94330154173584 y[1] (numeric) = 20.94330154178741 absolute error = 5.156408633411047e-11 relative error = 2.462080118139611e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.14999999999991 y[1] (closed_form) = 20.95560923559717 y[1] (numeric) = 20.95560923564873 absolute error = 5.156408633411047e-11 relative error = 2.460634083905271e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.19999999999991 y[1] (closed_form) = 20.96790180014447 y[1] (numeric) = 20.96790180019603 absolute error = 5.156408633411047e-11 relative error = 2.459191521669335e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.24999999999991 y[1] (closed_form) = 20.98017927252769 y[1] (numeric) = 20.98017927257926 absolute error = 5.156408633411047e-11 relative error = 2.457752417856152e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.2999999999999 y[1] (closed_form) = 20.99244168976013 y[1] (numeric) = 20.9924416898117 absolute error = 5.156408633411047e-11 relative error = 2.456316758962957e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.3499999999999 y[1] (closed_form) = 21.00468908871909 y[1] (numeric) = 21.00468908877066 absolute error = 5.156763904778927e-11 relative error = 2.455053670634169e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.3999999999999 y[1] (closed_form) = 21.01692150614653 y[1] (numeric) = 21.0169215061981 absolute error = 5.156763904778927e-11 relative error = 2.453624762918204e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.4499999999999 y[1] (closed_form) = 21.02913897864976 y[1] (numeric) = 21.02913897870132 absolute error = 5.156408633411047e-11 relative error = 2.452030317858563e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 40.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.49999999999989 y[1] (closed_form) = 21.04134154270205 y[1] (numeric) = 21.04134154275362 absolute error = 5.156763904778927e-11 relative error = 2.450777149505228e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.54999999999989 y[1] (closed_form) = 21.05352923464334 y[1] (numeric) = 21.05352923469491 absolute error = 5.156763904778927e-11 relative error = 2.449358417444583e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.59999999999989 y[1] (closed_form) = 21.06570209068086 y[1] (numeric) = 21.06570209073243 absolute error = 5.156763904778927e-11 relative error = 2.447943051022354e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.64999999999988 y[1] (closed_form) = 21.07786014688976 y[1] (numeric) = 21.07786014694133 absolute error = 5.156763904778927e-11 relative error = 2.446531037231432e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.69999999999988 y[1] (closed_form) = 21.09000343921377 y[1] (numeric) = 21.09000343926535 absolute error = 5.157119176146807e-11 relative error = 2.445290817998587e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.74999999999988 y[1] (closed_form) = 21.10213200346587 y[1] (numeric) = 21.10213200351744 absolute error = 5.157119176146807e-11 relative error = 2.4438853739043e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.79999999999988 y[1] (closed_form) = 21.11424587532884 y[1] (numeric) = 21.11424587538041 absolute error = 5.157119176146807e-11 relative error = 2.442483244060682e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.84999999999987 y[1] (closed_form) = 21.12634509035597 y[1] (numeric) = 21.12634509040754 absolute error = 5.157474447514687e-11 relative error = 2.441252580821014e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.89999999999987 y[1] (closed_form) = 21.13842968397165 y[1] (numeric) = 21.13842968402323 absolute error = 5.157474447514687e-11 relative error = 2.439856945204106e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.94999999999987 y[1] (closed_form) = 21.15049969147201 y[1] (numeric) = 21.15049969152358 absolute error = 5.157119176146807e-11 relative error = 2.438296613023372e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 39.99999999999986 y[1] (closed_form) = 21.16255514802549 y[1] (numeric) = 21.16255514807706 absolute error = 5.157119176146807e-11 relative error = 2.436907613506196e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.04999999999986 y[1] (closed_form) = 21.17459608867354 y[1] (numeric) = 21.17459608872511 absolute error = 5.157474447514687e-11 relative error = 2.435689647120807e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.09999999999986 y[1] (closed_form) = 21.18662254833114 y[1] (numeric) = 21.18662254838272 absolute error = 5.157119176146807e-11 relative error = 2.43413935580451e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.14999999999986 y[1] (closed_form) = 21.19863456178748 y[1] (numeric) = 21.19863456183906 absolute error = 5.157829718882567e-11 relative error = 2.433095256135052e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.19999999999985 y[1] (closed_form) = 21.21063216370652 y[1] (numeric) = 21.2106321637581 absolute error = 5.157829718882567e-11 relative error = 2.431718997846807e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.24999999999985 y[1] (closed_form) = 21.22261538862761 y[1] (numeric) = 21.22261538867919 absolute error = 5.158184990250447e-11 relative error = 2.430513344276372e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.29999999999985 y[1] (closed_form) = 21.23458427096607 y[1] (numeric) = 21.23458427101765 absolute error = 5.158184990250447e-11 relative error = 2.429143384409558e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.34999999999985 y[1] (closed_form) = 21.24653884501381 y[1] (numeric) = 21.24653884506539 absolute error = 5.158184990250447e-11 relative error = 2.427776602992908e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.39999999999984 y[1] (closed_form) = 21.25847914493988 y[1] (numeric) = 21.25847914499147 absolute error = 5.158540261618327e-11 relative error = 2.426580107846617e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.44999999999984 y[1] (closed_form) = 21.27040520479111 y[1] (numeric) = 21.2704052048427 absolute error = 5.158540261618327e-11 relative error = 2.425219553624854e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 41.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.49999999999984 y[1] (closed_form) = 21.28231705849264 y[1] (numeric) = 21.28231705854423 absolute error = 5.158184990250447e-11 relative error = 2.423695209536449e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.54999999999983 y[1] (closed_form) = 21.29421473984853 y[1] (numeric) = 21.29421473990011 absolute error = 5.158540261618327e-11 relative error = 2.422507861708087e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.59999999999983 y[1] (closed_form) = 21.30609828254232 y[1] (numeric) = 21.3060982825939 absolute error = 5.158540261618327e-11 relative error = 2.421156700401174e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.64999999999983 y[1] (closed_form) = 21.3179677201376 y[1] (numeric) = 21.31796772018919 absolute error = 5.158540261618327e-11 relative error = 2.419808646555653e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.69999999999983 y[1] (closed_form) = 21.32982308607862 y[1] (numeric) = 21.3298230861302 absolute error = 5.158895532986207e-11 relative error = 2.418630249377584e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.74999999999982 y[1] (closed_form) = 21.34166441369078 y[1] (numeric) = 21.34166441374237 absolute error = 5.158895532986207e-11 relative error = 2.417288283137256e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.79999999999982 y[1] (closed_form) = 21.35349173618128 y[1] (numeric) = 21.35349173623286 absolute error = 5.158895532986207e-11 relative error = 2.415949389787617e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.84999999999982 y[1] (closed_form) = 21.36530508663959 y[1] (numeric) = 21.36530508669118 absolute error = 5.158540261618327e-11 relative error = 2.414447273605341e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.89999999999981 y[1] (closed_form) = 21.37710449803807 y[1] (numeric) = 21.37710449808966 absolute error = 5.159250804354087e-11 relative error = 2.413446968380394e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.94999999999981 y[1] (closed_form) = 21.38889000323251 y[1] (numeric) = 21.38889000328411 absolute error = 5.159250804354087e-11 relative error = 2.412117133509204e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 40.99999999999981 y[1] (closed_form) = 21.40066163496266 y[1] (numeric) = 21.40066163501426 absolute error = 5.159250804354087e-11 relative error = 2.410790326185674e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.04999999999981 y[1] (closed_form) = 21.41241942585278 y[1] (numeric) = 21.41241942590437 absolute error = 5.159250804354087e-11 relative error = 2.409466535166477e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.0999999999998 y[1] (closed_form) = 21.4241634084122 y[1] (numeric) = 21.42416340846379 absolute error = 5.159250804354087e-11 relative error = 2.408145749265667e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.1499999999998 y[1] (closed_form) = 21.43589361503583 y[1] (numeric) = 21.43589361508743 absolute error = 5.159606075721967e-11 relative error = 2.406993694026758e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.1999999999998 y[1] (closed_form) = 21.44761007800474 y[1] (numeric) = 21.44761007805634 absolute error = 5.159606075721967e-11 relative error = 2.405678794493434e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.24999999999979 y[1] (closed_form) = 21.45931282948664 y[1] (numeric) = 21.45931282953824 absolute error = 5.159606075721967e-11 relative error = 2.404366867065891e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.29999999999979 y[1] (closed_form) = 21.47100190153646 y[1] (numeric) = 21.47100190158806 absolute error = 5.159606075721967e-11 relative error = 2.403057900783264e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.34999999999979 y[1] (closed_form) = 21.48267732609684 y[1] (numeric) = 21.48267732614843 absolute error = 5.159606075721967e-11 relative error = 2.401751884740248e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.39999999999979 y[1] (closed_form) = 21.49433913499866 y[1] (numeric) = 21.49433913505026 absolute error = 5.159606075721967e-11 relative error = 2.400448808086738e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.44999999999978 y[1] (closed_form) = 21.50598735996159 y[1] (numeric) = 21.50598736001319 absolute error = 5.159606075721967e-11 relative error = 2.399148660027475e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 42.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.49999999999978 y[1] (closed_form) = 21.51762203259457 y[1] (numeric) = 21.51762203264617 absolute error = 5.159606075721967e-11 relative error = 2.397851429821694e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.54999999999978 y[1] (closed_form) = 21.52924318439634 y[1] (numeric) = 21.52924318444794 absolute error = 5.159606075721967e-11 relative error = 2.396557106782775e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.59999999999977 y[1] (closed_form) = 21.54085084675597 y[1] (numeric) = 21.54085084680756 absolute error = 5.159606075721967e-11 relative error = 2.395265680277898e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.64999999999977 y[1] (closed_form) = 21.55244505095332 y[1] (numeric) = 21.55244505100491 absolute error = 5.159250804354087e-11 relative error = 2.393812299326976e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.69999999999977 y[1] (closed_form) = 21.56402582815959 y[1] (numeric) = 21.56402582821119 absolute error = 5.159606075721967e-11 relative error = 2.392691474605937e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.74999999999977 y[1] (closed_form) = 21.57559320943783 y[1] (numeric) = 21.57559320948942 absolute error = 5.159606075721967e-11 relative error = 2.391408674439133e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.79999999999976 y[1] (closed_form) = 21.58714722574338 y[1] (numeric) = 21.58714722579498 absolute error = 5.159961347089848e-11 relative error = 2.390293304219662e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.84999999999976 y[1] (closed_form) = 21.59868790792445 y[1] (numeric) = 21.59868790797605 absolute error = 5.159961347089848e-11 relative error = 2.389016114815328e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.89999999999976 y[1] (closed_form) = 21.61021528672254 y[1] (numeric) = 21.61021528677413 absolute error = 5.159606075721967e-11 relative error = 2.387577359718422e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.94999999999975 y[1] (closed_form) = 21.62172939277295 y[1] (numeric) = 21.62172939282455 absolute error = 5.160316618457728e-11 relative error = 2.386634540057911e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 41.99999999999975 y[1] (closed_form) = 21.63323025660532 y[1] (numeric) = 21.63323025665693 absolute error = 5.160316618457728e-11 relative error = 2.385365734681309e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.04999999999975 y[1] (closed_form) = 21.64471790864406 y[1] (numeric) = 21.64471790869566 absolute error = 5.160316618457728e-11 relative error = 2.384099732894601e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.09999999999975 y[1] (closed_form) = 21.65619237920883 y[1] (numeric) = 21.65619237926043 absolute error = 5.160316618457728e-11 relative error = 2.382836524583114e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.14999999999974 y[1] (closed_form) = 21.66765369851505 y[1] (numeric) = 21.66765369856665 absolute error = 5.160671889825608e-11 relative error = 2.38174006361348e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.19999999999974 y[1] (closed_form) = 21.67910189667438 y[1] (numeric) = 21.67910189672599 absolute error = 5.160316618457728e-11 relative error = 2.380318448177658e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.24999999999974 y[1] (closed_form) = 21.69053700369517 y[1] (numeric) = 21.69053700374678 absolute error = 5.160316618457728e-11 relative error = 2.379063560103939e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.29999999999973 y[1] (closed_form) = 21.70195904948294 y[1] (numeric) = 21.70195904953455 absolute error = 5.160671889825608e-11 relative error = 2.377975130290628e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.34999999999973 y[1] (closed_form) = 21.71336806384086 y[1] (numeric) = 21.71336806389246 absolute error = 5.160316618457728e-11 relative error = 2.376562034634862e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.39999999999973 y[1] (closed_form) = 21.72476407647019 y[1] (numeric) = 21.7247640765218 absolute error = 5.160671889825608e-11 relative error = 2.375478910454574e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.44999999999973 y[1] (closed_form) = 21.7361471169708 y[1] (numeric) = 21.7361471170224 absolute error = 5.160671889825608e-11 relative error = 2.374234891792916e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 43.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.49999999999972 y[1] (closed_form) = 21.74751721484155 y[1] (numeric) = 21.74751721489316 absolute error = 5.161027161193488e-11 relative error = 2.373156949461502e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.54999999999972 y[1] (closed_form) = 21.75887439948082 y[1] (numeric) = 21.75887439953243 absolute error = 5.161382432561368e-11 relative error = 2.372081541444314e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.59999999999972 y[1] (closed_form) = 21.77021870018694 y[1] (numeric) = 21.77021870023855 absolute error = 5.161027161193488e-11 relative error = 2.37068227575921e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.64999999999971 y[1] (closed_form) = 21.78155014615862 y[1] (numeric) = 21.78155014621024 absolute error = 5.161382432561368e-11 relative error = 2.369612078996878e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.69999999999971 y[1] (closed_form) = 21.79286876649546 y[1] (numeric) = 21.79286876654707 absolute error = 5.161382432561368e-11 relative error = 2.368381367255568e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.74999999999971 y[1] (closed_form) = 21.80417459019832 y[1] (numeric) = 21.80417459024993 absolute error = 5.161382432561368e-11 relative error = 2.367153322502552e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.79999999999971 y[1] (closed_form) = 21.81546764616983 y[1] (numeric) = 21.81546764622145 absolute error = 5.161737703929248e-11 relative error = 2.366090788264858e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.8499999999997 y[1] (closed_form) = 21.82674796321482 y[1] (numeric) = 21.82674796326643 absolute error = 5.161382432561368e-11 relative error = 2.364705196239027e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.8999999999997 y[1] (closed_form) = 21.83801557004072 y[1] (numeric) = 21.83801557009234 absolute error = 5.161737703929248e-11 relative error = 2.363647780804116e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.9499999999997 y[1] (closed_form) = 21.84927049525807 y[1] (numeric) = 21.84927049530968 absolute error = 5.161382432561368e-11 relative error = 2.362267625219588e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 42.99999999999969 y[1] (closed_form) = 21.86051276738088 y[1] (numeric) = 21.86051276743249 absolute error = 5.161737703929248e-11 relative error = 2.361215292091101e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.04999999999969 y[1] (closed_form) = 21.87174241482711 y[1] (numeric) = 21.87174241487873 absolute error = 5.161737703929248e-11 relative error = 2.36000296914161e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.09999999999969 y[1] (closed_form) = 21.88295946591911 y[1] (numeric) = 21.88295946597073 absolute error = 5.162092975297128e-11 relative error = 2.358955598915521e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.14999999999969 y[1] (closed_form) = 21.89416394888401 y[1] (numeric) = 21.89416394893563 absolute error = 5.162092975297128e-11 relative error = 2.357748387811927e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.19999999999968 y[1] (closed_form) = 21.90535589185416 y[1] (numeric) = 21.90535589190578 absolute error = 5.162092975297128e-11 relative error = 2.356543760704993e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.24999999999968 y[1] (closed_form) = 21.91653532286757 y[1] (numeric) = 21.91653532291919 absolute error = 5.162092975297128e-11 relative error = 2.355341708555108e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.29999999999968 y[1] (closed_form) = 21.92770226986832 y[1] (numeric) = 21.92770226991994 absolute error = 5.162448246665008e-11 relative error = 2.354304241789584e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.34999999999967 y[1] (closed_form) = 21.93885676070698 y[1] (numeric) = 21.9388567607586 absolute error = 5.162448246665008e-11 relative error = 2.353107230232287e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.39999999999967 y[1] (closed_form) = 21.94999882314101 y[1] (numeric) = 21.94999882319264 absolute error = 5.162803518032888e-11 relative error = 2.35207462179449e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.44999999999967 y[1] (closed_form) = 21.96112848483521 y[1] (numeric) = 21.96112848488684 absolute error = 5.162803518032888e-11 relative error = 2.35088261589014e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 44.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.49999999999967 y[1] (closed_form) = 21.97224577336212 y[1] (numeric) = 21.97224577341375 absolute error = 5.162803518032888e-11 relative error = 2.349693140740294e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.54999999999966 y[1] (closed_form) = 21.98335071620239 y[1] (numeric) = 21.98335071625402 absolute error = 5.162803518032888e-11 relative error = 2.348506187561183e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.59999999999966 y[1] (closed_form) = 21.99444334074525 y[1] (numeric) = 21.99444334079688 absolute error = 5.162803518032888e-11 relative error = 2.347321747610983e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.64999999999966 y[1] (closed_form) = 22.00552367428887 y[1] (numeric) = 22.00552367434049 absolute error = 5.162803518032888e-11 relative error = 2.346139812189555e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.69999999999965 y[1] (closed_form) = 22.01659174404078 y[1] (numeric) = 22.01659174409241 absolute error = 5.162803518032888e-11 relative error = 2.344960372638196e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.74999999999965 y[1] (closed_form) = 22.02764757711827 y[1] (numeric) = 22.0276475771699 absolute error = 5.162803518032888e-11 relative error = 2.343783420339387e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.79999999999965 y[1] (closed_form) = 22.0386912005488 y[1] (numeric) = 22.03869120060043 absolute error = 5.162803518032888e-11 relative error = 2.342608946716548e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.84999999999965 y[1] (closed_form) = 22.04972264127038 y[1] (numeric) = 22.04972264132201 absolute error = 5.162803518032888e-11 relative error = 2.341436943233784e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.89999999999964 y[1] (closed_form) = 22.06074192613194 y[1] (numeric) = 22.06074192618357 absolute error = 5.163514060768648e-11 relative error = 2.340589486091686e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.94999999999964 y[1] (closed_form) = 22.0717490818938 y[1] (numeric) = 22.07174908194543 absolute error = 5.163514060768648e-11 relative error = 2.33942223681967e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 43.99999999999964 y[1] (closed_form) = 22.08274413522796 y[1] (numeric) = 22.0827441352796 absolute error = 5.163869332136528e-11 relative error = 2.338418314551205e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.04999999999963 y[1] (closed_form) = 22.09372711271859 y[1] (numeric) = 22.09372711277023 absolute error = 5.163514060768648e-11 relative error = 2.337095065230616e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.09999999999963 y[1] (closed_form) = 22.10469804086232 y[1] (numeric) = 22.10469804091396 absolute error = 5.163869332136528e-11 relative error = 2.336095848308219e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.14999999999963 y[1] (closed_form) = 22.11565694606869 y[1] (numeric) = 22.11565694612033 absolute error = 5.164224603504408e-11 relative error = 2.335098892200174e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.19999999999963 y[1] (closed_form) = 22.12660385466051 y[1] (numeric) = 22.12660385471215 absolute error = 5.163869332136528e-11 relative error = 2.333783063164873e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.24999999999962 y[1] (closed_form) = 22.13753879287422 y[1] (numeric) = 22.13753879292586 absolute error = 5.164224603504408e-11 relative error = 2.332790764060323e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.29999999999962 y[1] (closed_form) = 22.14846178686031 y[1] (numeric) = 22.14846178691195 absolute error = 5.163869332136528e-11 relative error = 2.331479893199636e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.34999999999962 y[1] (closed_form) = 22.15937286268365 y[1] (numeric) = 22.15937286273529 absolute error = 5.163869332136528e-11 relative error = 2.330331893477218e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.39999999999961 y[1] (closed_form) = 22.17027204632391 y[1] (numeric) = 22.17027204637555 absolute error = 5.163869332136528e-11 relative error = 2.329186273107893e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.44999999999961 y[1] (closed_form) = 22.18115936367587 y[1] (numeric) = 22.18115936372751 absolute error = 5.163869332136528e-11 relative error = 2.328043024023776e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 45.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.49999999999961 y[1] (closed_form) = 22.19203484054986 y[1] (numeric) = 22.1920348406015 absolute error = 5.163869332136528e-11 relative error = 2.326902138194634e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.54999999999961 y[1] (closed_form) = 22.20289850267207 y[1] (numeric) = 22.20289850272371 absolute error = 5.163869332136528e-11 relative error = 2.325763607627656e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.5999999999996 y[1] (closed_form) = 22.21375037568494 y[1] (numeric) = 22.21375037573658 absolute error = 5.163869332136528e-11 relative error = 2.324627424367239e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.6499999999996 y[1] (closed_form) = 22.22459048514752 y[1] (numeric) = 22.22459048519917 absolute error = 5.164579874872288e-11 relative error = 2.323813290653759e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.6999999999996 y[1] (closed_form) = 22.23541885653584 y[1] (numeric) = 22.23541885658749 absolute error = 5.164224603504408e-11 relative error = 2.322521845360446e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.74999999999959 y[1] (closed_form) = 22.24623551524325 y[1] (numeric) = 22.2462355152949 absolute error = 5.164579874872288e-11 relative error = 2.321552278511791e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.79999999999959 y[1] (closed_form) = 22.25704048658079 y[1] (numeric) = 22.25704048663244 absolute error = 5.164579874872288e-11 relative error = 2.320425250601541e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.84999999999959 y[1] (closed_form) = 22.26783379577755 y[1] (numeric) = 22.26783379582919 absolute error = 5.164224603504408e-11 relative error = 2.319140986441013e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.89999999999959 y[1] (closed_form) = 22.27861546798101 y[1] (numeric) = 22.27861546803265 absolute error = 5.164224603504408e-11 relative error = 2.318018644797057e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.94999999999958 y[1] (closed_form) = 22.28938552825738 y[1] (numeric) = 22.28938552830903 absolute error = 5.164224603504408e-11 relative error = 2.316898595951629e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 44.99999999999958 y[1] (closed_form) = 22.30014400159202 y[1] (numeric) = 22.30014400164366 absolute error = 5.164224603504408e-11 relative error = 2.315780832238452e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.04999999999958 y[1] (closed_form) = 22.31089091288967 y[1] (numeric) = 22.31089091294131 absolute error = 5.164579874872288e-11 relative error = 2.314824582772961e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.09999999999958 y[1] (closed_form) = 22.32162628697491 y[1] (numeric) = 22.32162628702655 absolute error = 5.164579874872288e-11 relative error = 2.313711289882995e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.14999999999957 y[1] (closed_form) = 22.33235014859243 y[1] (numeric) = 22.33235014864408 absolute error = 5.164935146240168e-11 relative error = 2.312759343228238e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.19999999999957 y[1] (closed_form) = 22.34306252240742 y[1] (numeric) = 22.34306252245907 absolute error = 5.164935146240168e-11 relative error = 2.31165049153864e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.24999999999957 y[1] (closed_form) = 22.35376343300587 y[1] (numeric) = 22.35376343305752 absolute error = 5.164935146240168e-11 relative error = 2.310543887484296e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.29999999999956 y[1] (closed_form) = 22.36445290489491 y[1] (numeric) = 22.36445290494657 absolute error = 5.165290417608048e-11 relative error = 2.309598378987183e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.34999999999956 y[1] (closed_form) = 22.37513096250322 y[1] (numeric) = 22.37513096255487 absolute error = 5.165290417608048e-11 relative error = 2.308496172051089e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.39999999999956 y[1] (closed_form) = 22.38579763018124 y[1] (numeric) = 22.38579763023289 absolute error = 5.165645688975928e-11 relative error = 2.307554894542351e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.44999999999956 y[1] (closed_form) = 22.39645293220162 y[1] (numeric) = 22.39645293225328 absolute error = 5.165290417608048e-11 relative error = 2.306298427364537e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 46.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.49999999999955 y[1] (closed_form) = 22.40709689275949 y[1] (numeric) = 22.40709689281114 absolute error = 5.165645688975928e-11 relative error = 2.30536142798808e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.54999999999955 y[1] (closed_form) = 22.41772953597279 y[1] (numeric) = 22.41772953602445 absolute error = 5.165645688975928e-11 relative error = 2.30426800389702e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.59999999999955 y[1] (closed_form) = 22.42835088588262 y[1] (numeric) = 22.42835088593428 absolute error = 5.165645688975928e-11 relative error = 2.303176776241453e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.64999999999954 y[1] (closed_form) = 22.43896096645356 y[1] (numeric) = 22.43896096650522 absolute error = 5.166000960343808e-11 relative error = 2.302246065701092e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.69999999999954 y[1] (closed_form) = 22.449559801574 y[1] (numeric) = 22.44955980162566 absolute error = 5.166000960343808e-11 relative error = 2.301159134524146e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.74999999999954 y[1] (closed_form) = 22.46014741505642 y[1] (numeric) = 22.46014741510808 absolute error = 5.166356231711688e-11 relative error = 2.300232556910273e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.79999999999954 y[1] (closed_form) = 22.47072383063777 y[1] (numeric) = 22.47072383068943 absolute error = 5.166000960343808e-11 relative error = 2.298991790064283e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.84999999999953 y[1] (closed_form) = 22.48128907197977 y[1] (numeric) = 22.48128907203143 absolute error = 5.166356231711688e-11 relative error = 2.298069392360126e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.89999999999953 y[1] (closed_form) = 22.49184316266921 y[1] (numeric) = 22.49184316272087 absolute error = 5.166356231711688e-11 relative error = 2.296991044418511e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.94999999999953 y[1] (closed_form) = 22.50238612621827 y[1] (numeric) = 22.50238612626993 absolute error = 5.166356231711688e-11 relative error = 2.295914843311749e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 45.99999999999952 y[1] (closed_form) = 22.51291798606485 y[1] (numeric) = 22.51291798611652 absolute error = 5.166711503079569e-11 relative error = 2.294998589821934e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.04999999999952 y[1] (closed_form) = 22.52343876557289 y[1] (numeric) = 22.52343876562455 absolute error = 5.166356231711688e-11 relative error = 2.293768853630144e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.09999999999952 y[1] (closed_form) = 22.53394848803264 y[1] (numeric) = 22.53394848808431 absolute error = 5.166711503079569e-11 relative error = 2.292856711651539e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.14999999999952 y[1] (closed_form) = 22.54444717666101 y[1] (numeric) = 22.54444717671267 absolute error = 5.166711503079569e-11 relative error = 2.291788954766819e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.19999999999951 y[1] (closed_form) = 22.55493485460185 y[1] (numeric) = 22.55493485465352 absolute error = 5.166711503079569e-11 relative error = 2.290723310169708e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.24999999999951 y[1] (closed_form) = 22.56541154492629 y[1] (numeric) = 22.56541154497796 absolute error = 5.166711503079569e-11 relative error = 2.289659771014137e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.29999999999951 y[1] (closed_form) = 22.575877270633 y[1] (numeric) = 22.57587727068466 absolute error = 5.166711503079569e-11 relative error = 2.28859833048459e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.3499999999995 y[1] (closed_form) = 22.58633205464853 y[1] (numeric) = 22.58633205470019 absolute error = 5.166356231711688e-11 relative error = 2.287381686947435e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.3999999999995 y[1] (closed_form) = 22.59677591982759 y[1] (numeric) = 22.59677591987926 absolute error = 5.167066774447449e-11 relative error = 2.286638940342633e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.4499999999995 y[1] (closed_form) = 22.60720888895337 y[1] (numeric) = 22.60720888900503 absolute error = 5.166711503079569e-11 relative error = 2.285426532951706e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 47.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.4999999999995 y[1] (closed_form) = 22.6176309847378 y[1] (numeric) = 22.61763098478947 absolute error = 5.167066774447449e-11 relative error = 2.284530496555605e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.54999999999949 y[1] (closed_form) = 22.6280422298219 y[1] (numeric) = 22.62804222987358 absolute error = 5.167422045815329e-11 relative error = 2.283636380616742e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.59999999999949 y[1] (closed_form) = 22.63844264677605 y[1] (numeric) = 22.63844264682772 absolute error = 5.167066774447449e-11 relative error = 2.282430313369322e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.64999999999949 y[1] (closed_form) = 22.64883225810024 y[1] (numeric) = 22.64883225815191 absolute error = 5.167066774447449e-11 relative error = 2.281383302929216e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.69999999999948 y[1] (closed_form) = 22.65921108622443 y[1] (numeric) = 22.65921108627611 absolute error = 5.167422045815329e-11 relative error = 2.280495126750834e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.74999999999948 y[1] (closed_form) = 22.66957915350884 y[1] (numeric) = 22.66957915356051 absolute error = 5.167066774447449e-11 relative error = 2.279295411466728e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.79999999999948 y[1] (closed_form) = 22.67993648224416 y[1] (numeric) = 22.67993648229583 absolute error = 5.167422045815329e-11 relative error = 2.278411163038679e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.84999999999948 y[1] (closed_form) = 22.69028309465192 y[1] (numeric) = 22.6902830947036 absolute error = 5.167422045815329e-11 relative error = 2.277372223281465e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.89999999999947 y[1] (closed_form) = 22.70061901288475 y[1] (numeric) = 22.70061901293642 absolute error = 5.167422045815329e-11 relative error = 2.276335302963469e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.94999999999947 y[1] (closed_form) = 22.71094425902664 y[1] (numeric) = 22.71094425907831 absolute error = 5.167422045815329e-11 relative error = 2.275300395650215e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 46.99999999999947 y[1] (closed_form) = 22.72125885509326 y[1] (numeric) = 22.72125885514494 absolute error = 5.167422045815329e-11 relative error = 2.274267494935469e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.04999999999946 y[1] (closed_form) = 22.73156282303223 y[1] (numeric) = 22.7315628230839 absolute error = 5.167066774447449e-11 relative error = 2.273080304541155e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.09999999999946 y[1] (closed_form) = 22.74185618472337 y[1] (numeric) = 22.74185618477504 absolute error = 5.166711503079569e-11 relative error = 2.271895249496063e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.14999999999946 y[1] (closed_form) = 22.75213896197902 y[1] (numeric) = 22.7521389620307 absolute error = 5.167422045815329e-11 relative error = 2.271180768740284e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.19999999999946 y[1] (closed_form) = 22.76241117654433 y[1] (numeric) = 22.762411176596 absolute error = 5.167422045815329e-11 relative error = 2.2701558309166e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.24999999999945 y[1] (closed_form) = 22.77267285009745 y[1] (numeric) = 22.77267285014912 absolute error = 5.167066774447449e-11 relative error = 2.268976860318501e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.29999999999945 y[1] (closed_form) = 22.7829240042499 y[1] (numeric) = 22.78292400430157 absolute error = 5.167422045815329e-11 relative error = 2.268111873985711e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.34999999999945 y[1] (closed_form) = 22.7931646605468 y[1] (numeric) = 22.79316466059848 absolute error = 5.167422045815329e-11 relative error = 2.267092842425578e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.39999999999944 y[1] (closed_form) = 22.80339484046715 y[1] (numeric) = 22.80339484051882 absolute error = 5.167422045815329e-11 relative error = 2.266075767212155e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.44999999999944 y[1] (closed_form) = 22.81361456542408 y[1] (numeric) = 22.81361456547575 absolute error = 5.167422045815329e-11 relative error = 2.265060642186436e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 48.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.49999999999944 y[1] (closed_form) = 22.82382385676515 y[1] (numeric) = 22.82382385681683 absolute error = 5.167777317183209e-11 relative error = 2.264203119343406e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.54999999999944 y[1] (closed_form) = 22.83402273577261 y[1] (numeric) = 22.83402273582428 absolute error = 5.167422045815329e-11 relative error = 2.263036218195517e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.59999999999943 y[1] (closed_form) = 22.84421122366363 y[1] (numeric) = 22.84421122371531 absolute error = 5.167422045815329e-11 relative error = 2.262026907045296e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.64999999999943 y[1] (closed_form) = 22.85438934159064 y[1] (numeric) = 22.85438934164232 absolute error = 5.168132588551089e-11 relative error = 2.261330421612303e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.69999999999943 y[1] (closed_form) = 22.8645571106415 y[1] (numeric) = 22.86455711069319 absolute error = 5.168487859918969e-11 relative error = 2.260480198636114e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.74999999999942 y[1] (closed_form) = 22.87471455183986 y[1] (numeric) = 22.87471455189154 absolute error = 5.168132588551089e-11 relative error = 2.259321128068636e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.79999999999942 y[1] (closed_form) = 22.88486168614532 y[1] (numeric) = 22.88486168619701 absolute error = 5.168487859918969e-11 relative error = 2.258474589360534e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.84999999999942 y[1] (closed_form) = 22.89499853445378 y[1] (numeric) = 22.89499853450547 absolute error = 5.168843131286849e-11 relative error = 2.2576298153103e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.89999999999942 y[1] (closed_form) = 22.90512511759765 y[1] (numeric) = 22.90512511764933 absolute error = 5.168843131286849e-11 relative error = 2.256631694762369e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.94999999999941 y[1] (closed_form) = 22.91524145634609 y[1] (numeric) = 22.91524145639778 absolute error = 5.168487859918969e-11 relative error = 2.255480427629367e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 47.99999999999941 y[1] (closed_form) = 22.92534757140533 y[1] (numeric) = 22.92534757145701 absolute error = 5.168487859918969e-11 relative error = 2.254486150676991e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.04999999999941 y[1] (closed_form) = 22.93544348341885 y[1] (numeric) = 22.93544348347053 absolute error = 5.168132588551089e-11 relative error = 2.253338851846219e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.0999999999994 y[1] (closed_form) = 22.9455292129677 y[1] (numeric) = 22.94552921301938 absolute error = 5.168487859918969e-11 relative error = 2.252503227076581e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.1499999999994 y[1] (closed_form) = 22.9556047805707 y[1] (numeric) = 22.95560478062238 absolute error = 5.168487859918969e-11 relative error = 2.251514568805221e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.1999999999994 y[1] (closed_form) = 22.96567020668471 y[1] (numeric) = 22.96567020673639 absolute error = 5.168843131286849e-11 relative error = 2.250682468557932e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.2499999999994 y[1] (closed_form) = 22.97572551170489 y[1] (numeric) = 22.97572551175658 absolute error = 5.168843131286849e-11 relative error = 2.2496974594572e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.29999999999939 y[1] (closed_form) = 22.98577071596495 y[1] (numeric) = 22.98577071601664 absolute error = 5.169198402654729e-11 relative error = 2.24886886175386e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.34999999999939 y[1] (closed_form) = 22.99580583973735 y[1] (numeric) = 22.99580583978904 absolute error = 5.168843131286849e-11 relative error = 2.247732985445091e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.39999999999939 y[1] (closed_form) = 23.0058309032336 y[1] (numeric) = 23.0058309032853 absolute error = 5.169198402654729e-11 relative error = 2.246907935817336e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.44999999999938 y[1] (closed_form) = 23.0158459266045 y[1] (numeric) = 23.01584592665619 absolute error = 5.169198402654729e-11 relative error = 2.245930225262563e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 49.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.49999999999938 y[1] (closed_form) = 23.02585092994033 y[1] (numeric) = 23.02585092999203 absolute error = 5.169553674022609e-11 relative error = 2.245108634530713e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.54999999999938 y[1] (closed_form) = 23.03584593327117 y[1] (numeric) = 23.03584593332286 absolute error = 5.169553674022609e-11 relative error = 2.244134506280975e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.59999999999938 y[1] (closed_form) = 23.04583095656707 y[1] (numeric) = 23.04583095661876 absolute error = 5.169553674022609e-11 relative error = 2.243162194396601e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.64999999999937 y[1] (closed_form) = 23.05580601973832 y[1] (numeric) = 23.05580601979002 absolute error = 5.169553674022609e-11 relative error = 2.242191693318767e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.69999999999937 y[1] (closed_form) = 23.0657711426357 y[1] (numeric) = 23.06577114268741 absolute error = 5.170264216758369e-11 relative error = 2.241531048229922e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.74999999999937 y[1] (closed_form) = 23.07572634505073 y[1] (numeric) = 23.07572634510242 absolute error = 5.169908945390489e-11 relative error = 2.240410060374689e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.79999999999936 y[1] (closed_form) = 23.08567164671581 y[1] (numeric) = 23.08567164676751 absolute error = 5.169908945390489e-11 relative error = 2.239444892271941e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.84999999999936 y[1] (closed_form) = 23.09560706730458 y[1] (numeric) = 23.09560706735629 absolute error = 5.170264216758369e-11 relative error = 2.23863533947877e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.89999999999936 y[1] (closed_form) = 23.1055326264321 y[1] (numeric) = 23.1055326264838 absolute error = 5.170264216758369e-11 relative error = 2.237673677707705e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.94999999999936 y[1] (closed_form) = 23.11544834365505 y[1] (numeric) = 23.11544834370675 absolute error = 5.170619488126249e-11 relative error = 2.236867488467093e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 48.99999999999935 y[1] (closed_form) = 23.12535423847201 y[1] (numeric) = 23.12535423852372 absolute error = 5.170619488126249e-11 relative error = 2.235909311834132e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.04999999999935 y[1] (closed_form) = 23.13525033032367 y[1] (numeric) = 23.13525033037538 absolute error = 5.170619488126249e-11 relative error = 2.234952902735205e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.09999999999935 y[1] (closed_form) = 23.14513663859307 y[1] (numeric) = 23.14513663864477 absolute error = 5.170264216758369e-11 relative error = 2.233844758616493e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.14999999999934 y[1] (closed_form) = 23.1550131826058 y[1] (numeric) = 23.1550131826575 absolute error = 5.170264216758369e-11 relative error = 2.23289193402071e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.19999999999934 y[1] (closed_form) = 23.16487998163024 y[1] (numeric) = 23.16487998168195 absolute error = 5.170619488126249e-11 relative error = 2.232094227220928e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.24999999999934 y[1] (closed_form) = 23.17473705487783 y[1] (numeric) = 23.17473705492954 absolute error = 5.170619488126249e-11 relative error = 2.231144834947732e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.29999999999934 y[1] (closed_form) = 23.18458442150323 y[1] (numeric) = 23.18458442155493 absolute error = 5.170619488126249e-11 relative error = 2.230197183664248e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.34999999999933 y[1] (closed_form) = 23.19442210060456 y[1] (numeric) = 23.19442210065626 absolute error = 5.170619488126249e-11 relative error = 2.229251268127727e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.39999999999933 y[1] (closed_form) = 23.20425011122364 y[1] (numeric) = 23.20425011127534 absolute error = 5.170619488126249e-11 relative error = 2.228307083117191e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.44999999999933 y[1] (closed_form) = 23.2140684723462 y[1] (numeric) = 23.21406847239791 absolute error = 5.170974759494129e-11 relative error = 2.227517664839346e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 50.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.49999999999932 y[1] (closed_form) = 23.22387720290212 y[1] (numeric) = 23.22387720295383 absolute error = 5.170974759494129e-11 relative error = 2.226576860666465e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.54999999999932 y[1] (closed_form) = 23.23367632176561 y[1] (numeric) = 23.23367632181732 absolute error = 5.170974759494129e-11 relative error = 2.225637771603925e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.59999999999932 y[1] (closed_form) = 23.24346584775545 y[1] (numeric) = 23.24346584780716 absolute error = 5.170974759494129e-11 relative error = 2.224700392516323e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.64999999999932 y[1] (closed_form) = 23.25324579963522 y[1] (numeric) = 23.25324579968693 absolute error = 5.171330030862009e-11 relative error = 2.223917501849627e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.69999999999931 y[1] (closed_form) = 23.26301619611348 y[1] (numeric) = 23.2630161961652 absolute error = 5.171330030862009e-11 relative error = 2.222983463221753e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.74999999999931 y[1] (closed_form) = 23.27277705584404 y[1] (numeric) = 23.27277705589575 absolute error = 5.171330030862009e-11 relative error = 2.22205111940581e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.79999999999931 y[1] (closed_form) = 23.2825283974261 y[1] (numeric) = 23.28252839747782 absolute error = 5.171330030862009e-11 relative error = 2.221120465350191e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.84999999999931 y[1] (closed_form) = 23.29227023940454 y[1] (numeric) = 23.29227023945625 absolute error = 5.171330030862009e-11 relative error = 2.220191496024053e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.8999999999993 y[1] (closed_form) = 23.30200260027006 y[1] (numeric) = 23.30200260032177 absolute error = 5.171685302229889e-11 relative error = 2.21941667029509e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.9499999999993 y[1] (closed_form) = 23.31172549845945 y[1] (numeric) = 23.31172549851117 absolute error = 5.171685302229889e-11 relative error = 2.218490991827979e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 49.9999999999993 y[1] (closed_form) = 23.32143895235577 y[1] (numeric) = 23.32143895240748 absolute error = 5.171685302229889e-11 relative error = 2.217566983236033e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.04999999999929 y[1] (closed_form) = 23.33114298028855 y[1] (numeric) = 23.33114298034027 absolute error = 5.171685302229889e-11 relative error = 2.216644639570045e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.09999999999929 y[1] (closed_form) = 23.34083760053403 y[1] (numeric) = 23.34083760058575 absolute error = 5.172040573597769e-11 relative error = 2.215876166106153e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.14999999999929 y[1] (closed_form) = 23.35052283131533 y[1] (numeric) = 23.35052283136705 absolute error = 5.172040573597769e-11 relative error = 2.214957074392166e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.19999999999929 y[1] (closed_form) = 23.36019869080269 y[1] (numeric) = 23.36019869085441 absolute error = 5.172040573597769e-11 relative error = 2.214039632990831e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.24999999999928 y[1] (closed_form) = 23.36986519711364 y[1] (numeric) = 23.36986519716536 absolute error = 5.172395844965649e-11 relative error = 2.213275858178455e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.29999999999928 y[1] (closed_form) = 23.37952236831323 y[1] (numeric) = 23.37952236836495 absolute error = 5.172040573597769e-11 relative error = 2.212209681668924e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.34999999999928 y[1] (closed_form) = 23.38917022241422 y[1] (numeric) = 23.38917022246594 absolute error = 5.172040573597769e-11 relative error = 2.211297162069186e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.39999999999927 y[1] (closed_form) = 23.39880877737729 y[1] (numeric) = 23.39880877742901 absolute error = 5.172040573597769e-11 relative error = 2.21038627342357e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.44999999999927 y[1] (closed_form) = 23.40843805111122 y[1] (numeric) = 23.40843805116294 absolute error = 5.172040573597769e-11 relative error = 2.209477010941466e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 51.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.49999999999927 y[1] (closed_form) = 23.41805806147313 y[1] (numeric) = 23.41805806152485 absolute error = 5.172395844965649e-11 relative error = 2.208721078147449e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.54999999999927 y[1] (closed_form) = 23.42766882626864 y[1] (numeric) = 23.42766882632036 absolute error = 5.172395844965649e-11 relative error = 2.207814991462582e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.59999999999926 y[1] (closed_form) = 23.43727036325207 y[1] (numeric) = 23.43727036330379 absolute error = 5.172395844965649e-11 relative error = 2.206910516796183e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.64999999999926 y[1] (closed_form) = 23.44686269012667 y[1] (numeric) = 23.4468626901784 absolute error = 5.172395844965649e-11 relative error = 2.206007649434358e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.69999999999926 y[1] (closed_form) = 23.45644582454479 y[1] (numeric) = 23.45644582459651 absolute error = 5.172395844965649e-11 relative error = 2.205106384682228e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.74999999999925 y[1] (closed_form) = 23.46601978410806 y[1] (numeric) = 23.46601978415978 absolute error = 5.172395844965649e-11 relative error = 2.204206717863829e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.79999999999925 y[1] (closed_form) = 23.47558458636762 y[1] (numeric) = 23.47558458641935 absolute error = 5.172751116333529e-11 relative error = 2.203459980859164e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.84999999999925 y[1] (closed_form) = 23.48514024882432 y[1] (numeric) = 23.48514024887604 absolute error = 5.172395844965649e-11 relative error = 2.202412159418372e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.89999999999925 y[1] (closed_form) = 23.49468678892882 y[1] (numeric) = 23.49468678898054 absolute error = 5.172751116333529e-11 relative error = 2.201668472027061e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.94999999999924 y[1] (closed_form) = 23.50422422408192 y[1] (numeric) = 23.50422422413364 absolute error = 5.172395844965649e-11 relative error = 2.200623937064949e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 50.99999999999924 y[1] (closed_form) = 23.51375257163463 y[1] (numeric) = 23.51375257168636 absolute error = 5.172751116333529e-11 relative error = 2.199883281315794e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.04999999999924 y[1] (closed_form) = 23.52327184888846 y[1] (numeric) = 23.52327184894018 absolute error = 5.172395844965649e-11 relative error = 2.198842014067044e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.09999999999923 y[1] (closed_form) = 23.5327820730955 y[1] (numeric) = 23.53278207314722 absolute error = 5.172395844965649e-11 relative error = 2.19795340342659e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.14999999999923 y[1] (closed_form) = 23.5422832614587 y[1] (numeric) = 23.54228326151042 absolute error = 5.172395844965649e-11 relative error = 2.197066353981659e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.19999999999923 y[1] (closed_form) = 23.55177543113202 y[1] (numeric) = 23.55177543118375 absolute error = 5.172751116333529e-11 relative error = 2.196331708180227e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.24999999999923 y[1] (closed_form) = 23.56125859922061 y[1] (numeric) = 23.56125859927234 absolute error = 5.172751116333529e-11 relative error = 2.195447706899936e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.29999999999922 y[1] (closed_form) = 23.57073278278101 y[1] (numeric) = 23.57073278283274 absolute error = 5.173106387701409e-11 relative error = 2.194715979080841e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.34999999999922 y[1] (closed_form) = 23.58019799882132 y[1] (numeric) = 23.58019799887305 absolute error = 5.172751116333529e-11 relative error = 2.193684343359667e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.39999999999922 y[1] (closed_form) = 23.58965426430139 y[1] (numeric) = 23.58965426435312 absolute error = 5.173106387701409e-11 relative error = 2.192955576941183e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.44999999999921 y[1] (closed_form) = 23.599101596133 y[1] (numeric) = 23.59910159618473 absolute error = 5.173106387701409e-11 relative error = 2.192077680003329e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 52.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.49999999999921 y[1] (closed_form) = 23.60854001118007 y[1] (numeric) = 23.6085400112318 absolute error = 5.173106387701409e-11 relative error = 2.191201313275464e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.54999999999921 y[1] (closed_form) = 23.61796952625877 y[1] (numeric) = 23.6179695263105 absolute error = 5.173461659069289e-11 relative error = 2.190476896550047e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.59999999999921 y[1] (closed_form) = 23.62739015813778 y[1] (numeric) = 23.62739015818951 absolute error = 5.173461659069289e-11 relative error = 2.189603517122876e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.6499999999992 y[1] (closed_form) = 23.63680192353842 y[1] (numeric) = 23.63680192359015 absolute error = 5.173461659069289e-11 relative error = 2.188731654901826e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.6999999999992 y[1] (closed_form) = 23.64620483913484 y[1] (numeric) = 23.64620483918657 absolute error = 5.173461659069289e-11 relative error = 2.187861305551718e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.7499999999992 y[1] (closed_form) = 23.65559892155419 y[1] (numeric) = 23.65559892160593 absolute error = 5.17381693043717e-11 relative error = 2.187142649651098e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.79999999999919 y[1] (closed_form) = 23.66498418737684 y[1] (numeric) = 23.66498418742857 absolute error = 5.173461659069289e-11 relative error = 2.186125128208989e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.84999999999919 y[1] (closed_form) = 23.67436065313647 y[1] (numeric) = 23.67436065318821 absolute error = 5.17381693043717e-11 relative error = 2.185409357507495e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.89999999999919 y[1] (closed_form) = 23.68372833532034 y[1] (numeric) = 23.68372833537208 absolute error = 5.17381693043717e-11 relative error = 2.184544957274013e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.94999999999919 y[1] (closed_form) = 23.69308725036939 y[1] (numeric) = 23.69308725042113 absolute error = 5.17417220180505e-11 relative error = 2.183831995859628e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 51.99999999999918 y[1] (closed_form) = 23.70243741467845 y[1] (numeric) = 23.70243741473019 absolute error = 5.17417220180505e-11 relative error = 2.182970515344885e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.04999999999918 y[1] (closed_form) = 23.71177884459642 y[1] (numeric) = 23.71177884464817 absolute error = 5.17417220180505e-11 relative error = 2.182110518032336e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.09999999999918 y[1] (closed_form) = 23.72111155642641 y[1] (numeric) = 23.72111155647815 absolute error = 5.17417220180505e-11 relative error = 2.181251999720598e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.14999999999917 y[1] (closed_form) = 23.73043556642592 y[1] (numeric) = 23.73043556647766 absolute error = 5.17417220180505e-11 relative error = 2.180394956224708e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.19999999999917 y[1] (closed_form) = 23.73975089080703 y[1] (numeric) = 23.73975089085878 absolute error = 5.17452747317293e-11 relative error = 2.179689035901683e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.24999999999917 y[1] (closed_form) = 23.74905754573657 y[1] (numeric) = 23.74905754578831 absolute error = 5.17452747317293e-11 relative error = 2.17883487090285e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.29999999999917 y[1] (closed_form) = 23.75835554733623 y[1] (numeric) = 23.75835554738798 absolute error = 5.17488274454081e-11 relative error = 2.178131703699086e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.34999999999916 y[1] (closed_form) = 23.76764491168282 y[1] (numeric) = 23.76764491173457 absolute error = 5.17523801590869e-11 relative error = 2.177429877945054e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.39999999999916 y[1] (closed_form) = 23.77692565480836 y[1] (numeric) = 23.77692565486011 absolute error = 5.17523801590869e-11 relative error = 2.176579971289145e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.44999999999916 y[1] (closed_form) = 23.78619779270028 y[1] (numeric) = 23.78619779275203 absolute error = 5.17523801590869e-11 relative error = 2.175731514978368e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 53.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.49999999999915 y[1] (closed_form) = 23.79546134130159 y[1] (numeric) = 23.79546134135334 absolute error = 5.17523801590869e-11 relative error = 2.174884504939634e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 54 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.54999999999915 y[1] (closed_form) = 23.80471631651101 y[1] (numeric) = 23.80471631656277 absolute error = 5.17559328727657e-11 relative error = 2.174188181224729e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 54.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.59999999999915 y[1] (closed_form) = 23.8139627341832 y[1] (numeric) = 23.81396273423495 absolute error = 5.17523801590869e-11 relative error = 2.173194807464788e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 54.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.64999999999915 y[1] (closed_form) = 23.82320061012884 y[1] (numeric) = 23.82320061018059 absolute error = 5.17523801590869e-11 relative error = 2.172352111961123e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 54.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.69999999999914 y[1] (closed_form) = 23.83242996011484 y[1] (numeric) = 23.8324299601666 absolute error = 5.17523801590869e-11 relative error = 2.171510846594239e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 54.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.74999999999914 y[1] (closed_form) = 23.84165079986453 y[1] (numeric) = 23.84165079991628 absolute error = 5.17523801590869e-11 relative error = 2.170671007369211e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 54.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.79999999999914 y[1] (closed_form) = 23.85086314505774 y[1] (numeric) = 23.85086314510949 absolute error = 5.17523801590869e-11 relative error = 2.169832590306518e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 54.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.84999999999913 y[1] (closed_form) = 23.86006701133102 y[1] (numeric) = 23.86006701138277 absolute error = 5.17523801590869e-11 relative error = 2.168995591441967e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 54.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.89999999999913 y[1] (closed_form) = 23.86926241427781 y[1] (numeric) = 23.86926241432956 absolute error = 5.17523801590869e-11 relative error = 2.168160006826618e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 54.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.94999999999913 y[1] (closed_form) = 23.87844936944853 y[1] (numeric) = 23.87844936950028 absolute error = 5.17523801590869e-11 relative error = 2.167325832526709e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 54.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 52.99999999999913 y[1] (closed_form) = 23.88762789235082 y[1] (numeric) = 23.88762789240257 absolute error = 5.17523801590869e-11 relative error = 2.166493064623582e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 54.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 53.04999999999912 y[1] (closed_form) = 23.89679799844964 y[1] (numeric) = 23.89679799850139 absolute error = 5.17523801590869e-11 relative error = 2.165661699213613e-10 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 54.55 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = 2.0 / ( 0.2 * x + 0.3 ) ; Iterations = 1000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Expected Time Remaining = -0.0 Seconds Optimized Time Remaining = -0.0 Seconds Expected Total Time = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = -8342 %