|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}\cos \left (y\right ) y^{\prime } = {\mathrm e}^{-x}-\sin \left (y\right ) \] |
exactWithIntegrationFactor |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
1.832 |
|
|
\[ {}y^{\prime } = x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right ) \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.08 |
|
|
\[ {}y^{\prime } = \frac {1}{y}-\frac {y}{2 x} \] |
exact, bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.885 |
|
|
\[ {}{\mathrm e}^{x y^{2}-x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{x y^{2}-x^{2}} x y y^{\prime } = 0 \] |
exact, bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
0.941 |
|
|
\[ {}2 x y+y^{2}+\left (2 x y+x^{2}\right ) y^{\prime } = 0 \] |
exact, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.411 |
|
|
\[ {}2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime } = 0 \] |
exact, bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.638 |
|
|
\[ {}2-2 x +3 y^{2} y^{\prime } = 0 \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
12.222 |
|
|
\[ {}1+3 x^{2} y^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime } = 0 \] |
exact, bernoulli, first_order_ode_lie_symmetry_lookup |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
1.307 |
|
|
\[ {}4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
2.842 |
|
|
\[ {}1+\ln \left (x y\right )+\frac {x y^{\prime }}{y} = 0 \] |
exact, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
✓ |
2.614 |
|
|
\[ {}1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.158 |
|
|
\[ {}{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+1\right ) y^{\prime } = 0 \] |
exact, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_exponential_symmetries], _exact] |
✓ |
✓ |
0.989 |
|
|
\[ {}1+y^{4}+x y^{3} y^{\prime } = 0 \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.348 |
|
|
\[ {}y+\left (y^{4}-3 x \right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.097 |
|
|
\[ {}\frac {2 y}{x}+\left (4 x^{2} y-3\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
8.607 |
|
|
\[ {}1+\left (1-x \tan \left (y\right )\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.204 |
|
|
\[ {}3 y+3 y^{2}+\left (2 x +4 x y\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.772 |
|
|
\[ {}2 x \left (y+1\right )-y^{\prime } = 0 \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.078 |
|
|
\[ {}2 y^{3}+\left (4 x^{3} y^{3}-3 x y^{2}\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
6.408 |
|
|
\[ {}4 x y+\left (3 x^{2}+5 y\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.204 |
|
|
\[ {}6+12 x^{2} y^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.278 |
|
|
\[ {}x y^{\prime } = 2 y-6 x^{3} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.721 |
|
|
\[ {}x y^{\prime } = 2 y^{2}-6 y \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.752 |
|
|
\[ {}4 y^{2}-x^{2} y^{2}+y^{\prime } = 0 \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.845 |
|
|
\[ {}y^{\prime } = \sqrt {x +y} \] |
homogeneousTypeC, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.669 |
|
|
\[ {}x^{2} y^{\prime }-\sqrt {x} = 3 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.18 |
|
|
\[ {}x y y^{\prime }-y^{2} = \sqrt {x^{4}+x^{2} y^{2}} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.862 |
|
|
\[ {}y^{\prime } = x^{2}-2 x y+y^{2} \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.462 |
|
|
\[ {}4 x y-6+x^{2} y^{\prime } = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.74 |
|
|
\[ {}x y^{2}-6+x^{2} y y^{\prime } = 0 \] |
exact, bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.003 |
|
|
\[ {}x^{3}+y^{3}+x y^{2} y^{\prime } = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.127 |
|
|
\[ {}3 y-x^{3}+x y^{\prime } = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.747 |
|
|
\[ {}1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime } = 0 \] |
exact, bernoulli, first_order_ode_lie_symmetry_lookup |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
1.183 |
|
|
\[ {}3 x y^{3}-y+x y^{\prime } = 0 \] |
bernoulli, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.03 |
|
|
\[ {}2+2 x^{2}-2 x y+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.832 |
|
|
\[ {}\left (y^{2}-4\right ) y^{\prime } = y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.355 |
|
|
\[ {}\left (x^{2}-4\right ) y^{\prime } = x \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.19 |
|
|
\[ {}y^{\prime } = \frac {1}{x y-3 x} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.931 |
|
|
\[ {}y^{\prime } = \frac {3 y}{1+x}-y^{2} \] |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
0.89 |
|
|
\[ {}\sin \left (y\right )+\left (x +y\right ) \cos \left (y\right ) y^{\prime } = 0 \] |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
10.493 |
|
|
\[ {}\sin \left (y\right )+\left (1+x \right ) \cos \left (y\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
10.951 |
|
|
\[ {}\sin \left (x \right )+2 \cos \left (x \right ) y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.235 |
|
|
\[ {}x y y^{\prime } = 2 x^{2}+2 y^{2} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.588 |
|
|
\[ {}y^{\prime } = \frac {2 y+x}{x +2 y+3} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.162 |
|
|
\[ {}y^{\prime } = \frac {2 y+x}{2 x -y} \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.306 |
|
|
\[ {}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right ) \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.951 |
|
|
\[ {}y^{\prime } = x y^{2}+3 y^{2}+x +3 \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.981 |
|
|
\[ {}1-\left (2 y+x \right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.086 |
|
|
\[ {}\ln \left (y\right )+\left (\frac {x}{y}+3\right ) y^{\prime } = 0 \] |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.429 |
|
|
\[ {}y^{2}+1-y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.144 |
|
|
\[ {}y^{\prime }-3 y = 12 \,{\mathrm e}^{2 x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.749 |
|
|
\[ {}x y y^{\prime } = x^{2}+x y+y^{2} \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.259 |
|
|
\[ {}\left (2+x \right ) y^{\prime }-x^{3} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.187 |
|
|
\[ {}x y^{3} y^{\prime } = y^{4}-x^{2} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.307 |
|
|
\[ {}y^{\prime } = 4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
1.252 |
|
|
\[ {}2 y-6 x +\left (1+x \right ) y^{\prime } = 0 \] |
linear, homogeneousTypeMapleC, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.564 |
|
|
\[ {}x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime } = 0 \] |
exact, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
2.127 |
|
|
\[ {}y y^{\prime }-x y^{2} = 6 x \,{\mathrm e}^{4 x^{2}} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
2.217 |
|
|
\[ {}\left (y-x +3\right )^{2} \left (y^{\prime }-1\right ) = 1 \] |
exact, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
1.268 |
|
|
\[ {}x +y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime } = 0 \] |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.372 |
|
|
\[ {}y^{2}-y^{2} \cos \left (x \right )+y^{\prime } = 0 \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.0 |
|
|
\[ {}y^{\prime }+2 y = \sin \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.923 |
|
|
\[ {}y^{\prime }+2 x = \sin \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.357 |
|
|
\[ {}y^{\prime } = y^{3}-y^{3} \cos \left (x \right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.077 |
|
|
\[ {}y^{2} {\mathrm e}^{x y^{2}}-2 x +2 x y \,{\mathrm e}^{x y^{2}} y^{\prime } = 0 \] |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
1.64 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{4 x +3 y} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.825 |
|
|
\[ {}y^{\prime } = \tan \left (6 x +3 y+1\right )-2 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
498.314 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{4 x +3 y} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.732 |
|
|
\[ {}y^{\prime } = x \left (6 y+{\mathrm e}^{x^{2}}\right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.832 |
|
|
\[ {}x \left (1-2 y\right )+\left (-x^{2}+y\right ) y^{\prime } = 0 \] |
exact, differentialType |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.736 |
|
|
\[ {}x^{2} y^{\prime }+3 x y = 6 \,{\mathrm e}^{-x^{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.908 |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime } = 18 x^{2} \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.438 |
|
|
\[ {}x y^{\prime \prime } = 2 y^{\prime } \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.237 |
|
|
\[ {}y^{\prime \prime } = y^{\prime } \] |
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]] |
✓ |
✓ |
0.737 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 8 \,{\mathrm e}^{2 x} \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_linear_constant_coeff |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.638 |
|
|
\[ {}x y^{\prime \prime } = y^{\prime }-2 x^{2} y^{\prime } \] |
kovacic, second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.319 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.174 |
|
|
\[ {}y^{\prime \prime } = 4 x \sqrt {y^{\prime }} \] |
second_order_ode_missing_y |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
1.045 |
|
|
\[ {}y^{\prime } y^{\prime \prime } = 1 \] |
second_order_integrable_as_is, second_order_ode_missing_x, second_order_ode_missing_y, exact nonlinear second order ode |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
2.463 |
|
|
\[ {}y y^{\prime \prime } = -{y^{\prime }}^{2} \] |
second_order_integrable_as_is, second_order_ode_missing_x, exact nonlinear second order ode |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.296 |
|
|
\[ {}x y^{\prime \prime } = {y^{\prime }}^{2}-y^{\prime } \] |
second_order_ode_missing_y |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.948 |
|
|
\[ {}x y^{\prime \prime }-{y^{\prime }}^{2} = 6 x^{5} \] |
second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.695 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime } \] |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.372 |
|
|
\[ {}y^{\prime \prime } = 2 y^{\prime }-6 \] |
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]] |
✓ |
✓ |
1.451 |
|
|
\[ {}\left (y-3\right ) y^{\prime \prime } = 2 {y^{\prime }}^{2} \] |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.821 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 9 \,{\mathrm e}^{-3 x} \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_linear_constant_coeff |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.694 |
|
|
\[ {}y^{\prime \prime \prime } = y^{\prime \prime } \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.199 |
|
|
\[ {}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x \] |
higher_order_missing_y |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.76 |
|
|
\[ {}y^{\prime \prime \prime } = 2 \sqrt {y^{\prime \prime }} \] |
unknown |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
N/A |
0.0 |
|
|
\[ {}y^{\prime \prime \prime \prime } = -2 y^{\prime \prime \prime } \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.233 |
|
|
\[ {}y y^{\prime \prime } = {y^{\prime }}^{2} \] |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.182 |
|
|
\[ {}3 y y^{\prime \prime } = 2 {y^{\prime }}^{2} \] |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.884 |
|
|
\[ {}\sin \left (y\right ) y^{\prime \prime }+\cos \left (y\right ) {y^{\prime }}^{2} = 0 \] |
second_order_integrable_as_is, second_order_ode_missing_x, exact nonlinear second order ode |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.275 |
|
|
\[ {}y^{\prime \prime } = y^{\prime } \] |
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]] |
✓ |
✓ |
0.634 |
|
|
\[ {}{y^{\prime }}^{2}+y y^{\prime \prime } = 2 y y^{\prime } \] |
second_order_integrable_as_is, second_order_ode_missing_x, exact nonlinear second order ode, second_order_nonlinear_solved_by_mainardi_lioville_method |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.186 |
|
|
\[ {}y^{2} y^{\prime \prime }+y^{\prime \prime }+2 y {y^{\prime }}^{2} = 0 \] |
second_order_integrable_as_is, second_order_ode_missing_x, exact nonlinear second order ode |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
602.552 |
|
|
\[ {}y^{\prime \prime } = 4 x \sqrt {y^{\prime }} \] |
second_order_ode_missing_y |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.939 |
|
|
\[ {}y^{\prime } y^{\prime \prime } = 1 \] |
second_order_integrable_as_is, second_order_ode_missing_x, second_order_ode_missing_y, exact nonlinear second order ode |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
1.559 |
|
|
\[ {}x y^{\prime \prime } = {y^{\prime }}^{2}-y^{\prime } \] |
second_order_ode_missing_y |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
0.815 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime } = 6 x^{5} \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.281 |
|
|
|
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