2.2.2 Performance using own ODE types classification

The types of the ODE’s are described in my ode solver page at ode types The following table gives count of the number of ODE’s for each ODE type, where the ODE type here is as classified by my own ode solver, and the percentage of solved ODE’s of that type for each CAS. It also gives a direct link to the ODE’s that failed if any.

Table 2.5: Percentage solved per own ODE type

Type of ODE	Count	Mathematica	Maple
first_order_ode_linear	1622	100.00%	100.00%
first_order_ode_separable	1433	99.16% [2496 , 2536 , 4111 , 7138 , 7139 , 7140 , 7141 , 10344 , 16710 , 16731 , 16732 , 17326 ]	99.79% [16731 , 17386 , 17389 ]
first_order_ode_poly	339	99.71% [12495 ]	99.71% [2909 ]
first_order_ode_homogA	1055	99.53% [3056 , 7429 , 12888 , 17948 , 19259 ]	99.91% [17386 ]
first_order_ode_homogC	34	100.00%	100.00%
first_order_ode_homogD	1429	99.79% [3056 , 7429 , 19225 ]	99.93% [17386 ]
first_order_ode_homogD2	1429	99.79% [3056 , 7429 , 19225 ]	99.93% [17386 ]
first_order_ode_homog_maple_C	1140	99.74% [3056 , 7429 , 12495 ]	99.82% [2909 , 17386 ]
first_order_ode_bernoulli	1067	99.91% [2536 ]	99.63% [7134 , 13730 , 17386 , 17389 ]
first_order_ode_exact	4732	99.34% [145 , 204 , 769 , 796 , 1535 , 2496 , 2536 , 4298 , 7129 , 7138 , 7139 , 7140 , 7141 , 10353 , 14646 , 14647 , 14650 , 14671 , 14672 , 14698 , 14701 , 14702 , 14703 , 15936 , 16057 , 16061 , 16062 , 16796 , 16797 , 16803 , 17326 ]	99.62% [2955 , 3034 , 4251 , 5270 , 5507 , 7134 , 7851 , 8488 , 10353 , 13730 , 16057 , 16061 , 16062 , 16789 , 17386 , 17389 , 18125 , 19157 ]
first_order_ode_clairaut	155	99.35% [18859 ]	99.35% [5687 ]
first_order_ode_dAlembert	1018	97.54% [31 , 2912 , 3321 , 4434 , 5595 , 5596 , 5597 , 5604 , 5618 , 5622 , 5649 , 5795 , 7429 , 8479 , 8481 , 8542 , 8546 , 12495 , 16173 , 16859 , 18842 , 18843 , 19550 , 19555 , 19574 ]	99.90% [7134 ]
first_order_ode_isobaric	1615	98.70% [204 , 2957 , 3054 , 3056 , 4390 , 4392 , 4393 , 4397 , 5634 , 5638 , 6689 , 7429 , 8475 , 12891 , 13884 , 16710 , 16854 , 17947 , 17968 , 18840 , 19571 ]	99.57% [5339 , 5384 , 10381 , 10396 , 10548 , 17386 , 18579 ]
first_order_ode_abel	40	97.50% [2868 ]	100.00%
first_order_ode_quadrature	473	99.58% [13863 , 19225 ]	100.00%
first_order_ode_autonomous	631	97.31% [1535 , 5610 , 5619 , 7129 , 13865 , 14646 , 14647 , 14650 , 14671 , 14672 , 14698 , 14701 , 14702 , 14703 , 15936 , 18560 , 19140 ]	99.68% [7134 , 13730 ]
first_order_ode_lie_symmetry	3944	99.24% [31 , 204 , 2957 , 3054 , 3056 , 4390 , 4392 , 4393 , 5634 , 5638 , 6689 , 7129 , 8475 , 12495 , 12888 , 12891 , 14646 , 14647 , 14650 , 14671 , 14672 , 14701 , 14702 , 14703 , 16173 , 16710 , 16854 , 18840 , 19259 , 19571 ]	99.70% [2909 , 5543 , 7134 , 10548 , 10800 , 10922 , 13730 , 17386 , 17432 , 18579 , 18835 , 19304 ]
first_order_ode_ID_1	63	100.00%	100.00%
first_order_ode_differential	38	97.37% [19225 ]	100.00%
first_order_ode_nonlinear_p_but_separable	34	100.00%	100.00%
first_order_ode_riccati	586	94.88% [4648 , 4983 , 12025 , 12068 , 12091 , 12128 , 12163 , 12180 , 12181 , 12193 , 12208 , 12212 , 12214 , 12217 , 12225 , 12231 , 12232 , 12233 , 12236 , 12245 , 12254 , 12263 , 12273 , 12275 , 12285 , 12297 , 12298 , 12303 , 12304 , 12305 ]	98.81% [12037 , 12163 , 12208 , 12273 , 12282 , 12285 , 12304 ]
first_order_ode_reduced_riccati	55	100.00%	100.00%
first_order_ode_time_varying_using_laplace	14	85.71% [9058 , 9061 ]	92.86% [9065 ]
first_order_ode_constant_coeff_using_laplace	81	100.00%	100.00%
first_order_ode_flip_role	25	96.00% [3002 ]	96.00% [5542 ]
second_order_linear_constant_coeff	2272	99.91% [17115 , 17189 ]	100.00%
second_order_euler_ode	516	100.00%	100.00%
second_order_nonlinear_exact_ode	59	84.75% [6012 , 6183 , 6184 , 6185 , 7914 , 15259 , 15260 , 16940 , 18196 ]	100.00%
second_order_linear_exact_ode	454	99.34% [12609 , 12750 , 13994 ]	100.00%
second_order_ode_missing_x	359	94.71% [3278 , 3279 , 6012 , 6183 , 6184 , 6185 , 6979 , 7768 , 7914 , 14231 , 15259 , 15260 , 16934 , 16940 , 16941 , 18196 , 18987 , 19399 , 19433 ]	99.16% [3279 , 11807 , 16947 ]
second_order_ode_missing_y	491	98.57% [3275 , 8524 , 8526 , 11826 , 13007 , 13934 , 16934 ]	99.39% [3275 , 3280 , 17986 ]
second_order_integrable_as_is	525	98.48% [6012 , 6183 , 7914 , 12609 , 12750 , 13994 , 15260 , 18196 ]	100.00%
second_order_integrable_as_is_ABC	524	98.47% [6012 , 6183 , 7914 , 12609 , 12750 , 13994 , 15260 , 18196 ]	100.00%
second_order_ode_can_be_made_integrable	251	98.80% [7768 , 8507 , 8508 ]	99.20% [8507 , 8508 ]
second_order_ode_solved_by_an_integrating_factor	447	100.00%	100.00%
second_order_airy	29	100.00%	100.00%
second_order_change_of_variable_on_x_method_2	629	99.84% [12706 ]	100.00%
second_order_change_of_variable_on_x_method_1	466	100.00%	100.00%
second_order_change_of_variable_on_y_method_1	208	99.52% [18036 ]	100.00%
second_order_change_of_variable_on_y_method_2	595	99.50% [11423 , 12603 , 17166 ]	99.83% [12603 ]
second_order_nonlinear_solved_by_mainardi_lioville_method	34	100.00%	100.00%
second_order_ode_non_constant_coeff_transformation_on_B	251	99.20% [12743 , 12761 ]	100.00%
second_order_bessel_ode	239	100.00%	100.00%
second_order_bessel_ode_form_A	10	100.00%	100.00%
second_order_kovacic	4348	99.84% [9236 , 9238 , 9656 , 9658 , 17189 , 18036 , 18948 ]	100.00%
second_order_adjoint	3421	99.82% [12557 , 13994 , 17116 , 17189 , 18036 , 18948 ]	100.00%
second_order_ode_constant_coeff_using_laplace	488	100.00%	99.80% [8181 ]
second_order_ode_time_varying_using_laplace	10	90.00% [18459 ]	100.00%
second_order_ode_flip_role	8	100.00%	100.00%
reduction_of_order	214	97.66% [2592 , 13786 , 16204 , 16205 , 19499 ]	98.13% [2592 , 13786 , 16204 , 16205 ]
higher_order_constant_coeff	972	100.00%	99.90% [2178 ]
higher_order_Euler_ode	156	100.00%	100.00%
higher_order_ode_constant_coeff_using_laplace	52	100.00%	100.00%
higher_order_ode_exact	65	100.00%	100.00%
higher_order_missing_y	36	100.00%	97.22% [16927 ]