|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime }+y \cot \left (x \right ) = 5 \,{\mathrm e}^{\cos \left (x \right )} \] |
linear |
[_linear] |
✓ |
✓ |
0.717 |
|
|
\[ {}\left (3 x +3 y-4\right ) y^{\prime } = -x -y \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.756 |
|
|
\[ {}x -x y^{2} = \left (x +x^{2} y\right ) y^{\prime } \] |
exactWithIntegrationFactor |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
8.067 |
|
|
\[ {}x -y-1+\left (4 y+x -1\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.734 |
|
|
\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.688 |
|
|
\[ {}y \left (x y+1\right )+x \left (1+x y+x^{2} y^{2}\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.46 |
|
|
\[ {}y^{\prime }+y = x y^{3} \] |
bernoulli |
[_Bernoulli] |
✓ |
✓ |
0.39 |
|
|
\[ {}y^{\prime }+y = y^{4} {\mathrm e}^{x} \] |
bernoulli |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
3.585 |
|
|
\[ {}2 y^{\prime }+y = y^{3} \left (-1+x \right ) \] |
bernoulli |
[_Bernoulli] |
✓ |
✓ |
0.32 |
|
|
\[ {}y^{\prime }-2 y \tan \left (x \right ) = y^{2} \tan \left (x \right )^{2} \] |
bernoulli |
[_Bernoulli] |
✓ |
✓ |
0.323 |
|
|
\[ {}y^{\prime }+y \tan \left (x \right ) = y^{3} \sec \left (x \right )^{4} \] |
bernoulli |
[_Bernoulli] |
✓ |
✓ |
2.615 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = x y+1 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.256 |
|
|
\[ {}x y y^{\prime }-\left (1+x \right ) \sqrt {y-1} = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.855 |
|
|
\[ {}x^{2}-2 x y+5 y^{2} = \left (x^{2}+2 x y+y^{2}\right ) y^{\prime } \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.461 |
|
|
\[ {}y^{\prime }-y \cot \left (x \right ) = y^{2} \sec \left (x \right )^{2} \] |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
2.363 |
|
|
\[ {}y+\left (x^{2}-4 x \right ) y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.238 |
|
|
\[ {}y^{\prime }-y \tan \left (x \right ) = \cos \left (x \right )-2 x \sin \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.78 |
|
|
\[ {}y^{\prime } = \frac {2 x y+y^{2}}{x^{2}+2 x y} \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.571 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = x \left (y+1\right ) \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.118 |
|
|
\[ {}x y^{\prime }+2 y = 3 x -1 \] |
linear, homogeneousTypeMapleC, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.792 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}-x y y^{\prime } \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.341 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{3 x -2 y} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.455 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = \sin \left (2 x \right ) \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.467 |
|
|
\[ {}y^{2}+x^{2} y^{\prime } = x y y^{\prime } \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.405 |
|
|
\[ {}2 x y y^{\prime } = x^{2}-y^{2} \] |
exact, bernoulli, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.6 |
|
|
\[ {}y^{\prime } = \frac {x -2 y+1}{2 x -4 y} \] |
exact, differentialType, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.503 |
|
|
\[ {}\left (-x^{3}+1\right ) y^{\prime }+x^{2} y = x^{2} \left (-x^{3}+1\right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.234 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = \sin \left (x \right ) \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.323 |
|
|
\[ {}y^{\prime }+x +x y^{2} = 0 \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.891 |
|
|
\[ {}y^{\prime }+\left (\frac {1}{x}-\frac {2 x}{-x^{2}+1}\right ) y = \frac {1}{-x^{2}+1} \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.244 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x y = \left (x^{2}+1\right )^{\frac {3}{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.305 |
|
|
\[ {}x \left (1+y^{2}\right )-y \left (x^{2}+1\right ) y^{\prime } = 0 \] |
exact, bernoulli, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.521 |
|
|
\[ {}\frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}} = 1 \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
7.163 |
|
|
\[ {}y^{\prime }+y \cot \left (x \right ) = \cos \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.926 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = x y^{2} \] |
riccati, bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.179 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 8 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.359 |
|
|
\[ {}y^{\prime \prime }-4 y = 10 \,{\mathrm e}^{3 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.385 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-2 x} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.441 |
|
|
\[ {}y^{\prime \prime }+25 y = 5 x^{2}+x \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.508 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.526 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 2 \,{\mathrm e}^{-2 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.164 |
|
|
\[ {}3 y^{\prime \prime }-2 y^{\prime }-y = 2 x -3 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.41 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = 8 \,{\mathrm e}^{4 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.446 |
|
|
\[ {}2 y^{\prime \prime }-7 y^{\prime }-4 y = {\mathrm e}^{3 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.399 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 54 x +18 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.457 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 100 \sin \left (4 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.511 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 4 \sinh \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.141 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 2 \cosh \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.29 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+10 y = 20-{\mathrm e}^{2 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.701 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \cos \left (x \right )^{2} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.655 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = x +{\mathrm e}^{2 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.418 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+3 y = x^{2}-1 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.653 |
|
|
\[ {}y^{\prime \prime }-9 y = {\mathrm e}^{3 x}+\sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.185 |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+3 x = {\mathrm e}^{-3 t} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.615 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 6 \sin \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.54 |
|
|
\[ {}x^{\prime \prime }-3 x^{\prime }+2 x = \sin \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.631 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 3 \sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.637 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+10 y = 50 x \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.528 |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.38 |
|
|
\[ {}y^{\prime \prime } = 3 \sin \left (x \right )-4 y \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.727 |
|
|
\[ {}\frac {x^{\prime \prime }}{2} = -48 x \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
3.251 |
|
|
\[ {}x^{\prime \prime }+5 x^{\prime }+6 x = \cos \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.664 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 4 x^{2} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.406 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.355 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = \sin \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.463 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.12 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.487 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.522 |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.546 |
|
|
\[ {}y^{\prime \prime } = 9 x^{2}+2 x -1 \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_quadrature, second_order_linear_constant_coeff |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.609 |
|
|
\[ {}y^{\prime \prime }-5 y = 2 \,{\mathrm e}^{5 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.451 |
|
|
\[ {}y^{\prime }-5 y = \left (-1+x \right ) \sin \left (x \right )+\left (1+x \right ) \cos \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.505 |
|
|
\[ {}y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.664 |
|
|
\[ {}y^{\prime }-5 y = x^{2} {\mathrm e}^{x}-x \,{\mathrm e}^{5 x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.688 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = x^{2}-1 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.451 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{2 x} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.434 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \cos \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.521 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.43 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.441 |
|
|
\[ {}y^{\prime }-y = {\mathrm e}^{x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.525 |
|
|
\[ {}y^{\prime }-y = {\mathrm e}^{2 x} x +1 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.573 |
|
|
\[ {}y^{\prime }-y = \sin \left (x \right )+\cos \left (2 x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.557 |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 1+{\mathrm e}^{x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.2 |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime } = \sec \left (x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
2.341 |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = \frac {{\mathrm e}^{x}}{1+{\mathrm e}^{-x}} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.316 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.964 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.356 |
|
|
\[ {}x^{\prime \prime }+4 x = \sin \left (2 t \right )^{2} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.809 |
|
|
\[ {}t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N = \ln \left (t \right ) t \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_1, second_order_change_of_variable_on_y_method_2, linear_second_order_ode_solved_by_an_integrating_factor, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.818 |
|
|
\[ {}y^{\prime }+\frac {4 y}{x} = x^{4} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.617 |
|
|
\[ {}y^{\prime \prime \prime \prime } = 5 x \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _quadrature]] |
✓ |
✓ |
0.188 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{5}} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.959 |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.994 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.352 |
|
|
\[ {}y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.501 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime } = -3 \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.546 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = \ln \left (x \right ) \] |
kovacic, second_order_euler_ode, exact linear second order ode, second_order_integrable_as_is, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.651 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime } = x^{3} {\mathrm e}^{x} \] |
kovacic, second_order_euler_ode, second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.254 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = x^{2} \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.075 |
|
|
\[ {}y^{\prime }+2 y = 0 \] |
first_order_laplace |
[_quadrature] |
✓ |
✓ |
0.33 |
|
|
|
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