|
Table 2.15: Summary of results
|
|||||||
|
type of ODE |
# problems |
Solved
| solved and verified
| not solved
| |||
|
|
|
# |
% |
# |
% |
# |
% |
|
|
|||||||
|
quadrature |
871 |
870 |
99.89% |
866 |
99.43% |
1 |
0.11% |
|
linear |
4812 |
4723 |
98.15% |
4722 |
98.13% |
89 |
1.85% |
|
separable |
1172 |
1172 |
100.00% |
1169 |
99.74% |
0 |
0.00% |
|
homogeneous |
1193 |
1192 |
99.92% |
1192 |
99.92% |
1 |
0.08% |
|
homogeneousTypeC |
26 |
26 |
100.00% |
26 |
100.00% |
0 |
0.00% |
|
homogeneousTypeMapleC |
175 |
175 |
100.00% |
175 |
100.00% |
0 |
0.00% |
|
homogeneousTypeD |
938 |
938 |
100.00% |
938 |
100.00% |
0 |
0.00% |
|
homogeneousTypeD2 |
938 |
938 |
100.00% |
938 |
100.00% |
0 |
0.00% |
|
exact |
3443 |
3435 |
99.77% |
3428 |
99.56% |
8 |
0.23% |
|
exactWithIntegrationFactor |
1335 |
1333 |
99.85% |
1329 |
99.55% |
2 |
0.15% |
|
exactByInspection |
105 |
105 |
100.00% |
105 |
100.00% |
0 |
0.00% |
|
bernoulli |
498 |
498 |
100.00% |
497 |
99.80% |
0 |
0.00% |
|
riccati |
917 |
894 |
97.49% |
882 |
96.18% |
23 |
2.51% |
|
clairaut |
115 |
115 |
100.00% |
115 |
100.00% |
0 |
0.00% |
|
dAlembert |
256 |
256 |
100.00% |
255 |
99.61% |
0 |
0.00% |
|
isobaric |
13 |
13 |
100.00% |
13 |
100.00% |
0 |
0.00% |
|
first order special form ID 1 |
39 |
39 |
100.00% |
39 |
100.00% |
0 |
0.00% |
|
polynomial |
16 |
16 |
100.00% |
16 |
100.00% |
0 |
0.00% |
|
abelFirstKind |
99 |
57 |
57.58% |
55 |
55.56% |
42 |
42.42% |
|
differentialType |
254 |
253 |
99.61% |
253 |
99.61% |
1 |
0.39% |
|
first order ode series method. Taylor series method |
83 |
83 |
100.00% |
83 |
100.00% |
0 |
0.00% |
|
first order ode series method. Ordinary point |
71 |
71 |
100.00% |
71 |
100.00% |
0 |
0.00% |
|
first order ode series method. Regular singular point |
8 |
8 |
100.00% |
8 |
100.00% |
0 |
0.00% |
|
first order ode series method. Irregular singular point |
3 |
0 |
0.00% |
0 |
0.00% |
3 |
100.00% |
|
first_order_laplace |
77 |
77 |
100.00% |
77 |
100.00% |
0 |
0.00% |
|
first_order_ode_lie_symmetry_lookup |
2268 |
2265 |
99.87% |
2260 |
99.65% |
3 |
0.13% |
|
first_order_ode_lie_symmetry_calculated |
1312 |
1312 |
100.00% |
1311 |
99.92% |
0 |
0.00% |
|
first_order_nonlinear_p_but_separable |
34 |
34 |
100.00% |
34 |
100.00% |
0 |
0.00% |
|
first_order_nonlinear_p_but_linear_in_x_y |
4 |
4 |
100.00% |
4 |
100.00% |
0 |
0.00% |
|
second_order_laplace |
331 |
331 |
100.00% |
328 |
99.09% |
0 |
0.00% |
|
reduction_of_order |
160 |
159 |
99.38% |
159 |
99.38% |
1 |
0.62% |
|
second_order_ode_quadrature |
43 |
42 |
97.67% |
42 |
97.67% |
1 |
2.33% |
|
second_order_linear_constant_coeff |
1711 |
1696 |
99.12% |
1696 |
99.12% |
15 |
0.88% |
|
second_order_airy |
23 |
23 |
100.00% |
23 |
100.00% |
0 |
0.00% |
|
second_order_euler_ode |
392 |
390 |
99.49% |
390 |
99.49% |
2 |
0.51% |
|
exact linear second order ode |
338 |
336 |
99.41% |
336 |
99.41% |
2 |
0.59% |
|
exact nonlinear second order ode |
50 |
49 |
98.00% |
49 |
98.00% |
1 |
2.00% |
|
second_order_change_of_variable_on_x_method_1 |
386 |
381 |
98.70% |
380 |
98.45% |
5 |
1.30% |
|
second_order_change_of_variable_on_x_method_2 |
466 |
461 |
98.93% |
460 |
98.71% |
5 |
1.07% |
|
second_order_change_of_variable_on_y_method_1 |
156 |
151 |
96.79% |
151 |
96.79% |
5 |
3.21% |
|
second_order_change_of_variable_on_y_method_2 |
444 |
438 |
98.65% |
438 |
98.65% |
6 |
1.35% |
|
second_order_integrable_as_is |
405 |
400 |
98.77% |
400 |
98.77% |
5 |
1.23% |
|
second_order_ode_can_be_made_integrable |
188 |
185 |
98.40% |
185 |
98.40% |
3 |
1.60% |
|
linear_second_order_ode_solved_by_an_integrating_factor |
337 |
331 |
98.22% |
331 |
98.22% |
6 |
1.78% |
|
second_order_ode_lagrange_adjoint_equation_method |
28 |
27 |
96.43% |
27 |
96.43% |
1 |
3.57% |
|
second_order_ode_non_constant_coeff_transformation_on_B |
189 |
188 |
99.47% |
188 |
99.47% |
1 |
0.53% |
|
second_order_nonlinear_solved_by_mainardi_lioville_method |
26 |
26 |
100.00% |
26 |
100.00% |
0 |
0.00% |
|
second_order_bessel_ode |
284 |
278 |
97.89% |
278 |
97.89% |
6 |
2.11% |
|
second_order_bessel_ode_form_A |
10 |
10 |
100.00% |
10 |
100.00% |
0 |
0.00% |
|
second_order_ode_missing_x |
297 |
273 |
91.92% |
267 |
89.90% |
24 |
8.08% |
|
second_order_ode_missing_y |
356 |
353 |
99.16% |
351 |
98.60% |
3 |
0.84% |
|
second order series method. Taylor series method |
582 |
582 |
100.00% |
582 |
100.00% |
0 |
0.00% |
|
second order series method. Ordinary point |
574 |
574 |
100.00% |
574 |
100.00% |
0 |
0.00% |
|
second order series method. Regular singular point. Difference not integer |
266 |
260 |
97.74% |
260 |
97.74% |
6 |
2.26% |
|
second order series method. Regular singular point. Repeated root |
208 |
207 |
99.52% |
207 |
99.52% |
1 |
0.48% |
|
second order series method. Regular singular point. Difference is integer |
322 |
321 |
99.69% |
321 |
99.69% |
1 |
0.31% |
|
second order series method. Irregular singular point |
38 |
0 |
0.00% |
0 |
0.00% |
38 |
100.00% |
|
second order series method. Regular singular point. Complex roots |
30 |
30 |
100.00% |
30 |
100.00% |
0 |
0.00% |
|
second_order_ode_high_degree |
7 |
7 |
100.00% |
7 |
100.00% |
0 |
0.00% |
|
higher_order_linear_constant_coefficients_ODE |
728 |
728 |
100.00% |
728 |
100.00% |
0 |
0.00% |
|
higher_order_ODE_non_constant_coefficients_of_type_Euler |
96 |
96 |
100.00% |
95 |
98.96% |
0 |
0.00% |
|
higher_order_laplace |
29 |
29 |
100.00% |
28 |
96.55% |
0 |
0.00% |
|
higher_order_missing_y |
35 |
35 |
100.00% |
35 |
100.00% |
0 |
0.00% |
|
unknown |
1303 |
0 |
0.00% |
0 |
0.00% |
1303 |
100.00% |
|
|
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|
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