|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}{y^{\prime }}^{2} x = {\mathrm e}^{\frac {1}{y^{\prime }}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.648 |
|
|
\[ {}x \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} = a \] |
quadrature |
[_quadrature] |
✓ |
✓ |
14.369 |
|
|
\[ {}y^{\frac {2}{5}}+{y^{\prime }}^{\frac {2}{5}} = a^{\frac {2}{5}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
3.309 |
|
|
\[ {}x = y^{\prime }+\sin \left (y^{\prime }\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.668 |
|
|
\[ {}y = y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.714 |
|
|
\[ {}y = \arcsin \left (y^{\prime }\right )+\ln \left (1+{y^{\prime }}^{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✗ |
1.055 |
|
|
\[ {}y = 2 x y^{\prime }+\ln \left (y^{\prime }\right ) \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
2.528 |
|
|
\[ {}y = x \left (1+y^{\prime }\right )+{y^{\prime }}^{2} \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.702 |
|
|
\[ {}y = 2 x y^{\prime }+\sin \left (y^{\prime }\right ) \] |
dAlembert |
[_dAlembert] |
✓ |
✓ |
1.829 |
|
|
\[ {}y = {y^{\prime }}^{2} x -\frac {1}{y^{\prime }} \] |
dAlembert |
[_dAlembert] |
✓ |
✓ |
151.895 |
|
|
\[ {}y = \frac {3 x y^{\prime }}{2}+{\mathrm e}^{y^{\prime }} \] |
dAlembert |
[_dAlembert] |
✓ |
✓ |
1.561 |
|
|
\[ {}y = x y^{\prime }+\frac {a}{{y^{\prime }}^{2}} \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.572 |
|
|
\[ {}y = x y^{\prime }+{y^{\prime }}^{2} \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.279 |
|
|
\[ {}{y^{\prime }}^{2} x -y y^{\prime }-y^{\prime }+1 = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
0.306 |
|
|
\[ {}y = x y^{\prime }+a \sqrt {1+{y^{\prime }}^{2}} \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.637 |
|
|
\[ {}x = \frac {y}{y^{\prime }}+\frac {1}{{y^{\prime }}^{2}} \] |
clairaut |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
0.299 |
|
|
\[ {}y^{\prime } {\mathrm e}^{-x}+y^{2}-2 \,{\mathrm e}^{x} y = 1-{\mathrm e}^{2 x} \] |
riccati |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.674 |
|
|
\[ {}y^{\prime }+y^{2}-2 y \sin \left (x \right )+\sin \left (x \right )^{2}-\cos \left (x \right ) = 0 \] |
riccati |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.881 |
|
|
\[ {}x y^{\prime }-y^{2}+\left (2 x +1\right ) y = x^{2}+2 x \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
0.905 |
|
|
\[ {}x^{2} y^{\prime } = x^{2} y^{2}+x y+1 \] |
riccati, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
0.944 |
|
|
\[ {}\left (1+{y^{\prime }}^{2}\right ) y^{2}-4 y y^{\prime }-4 x = 0 \] |
unknown |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
N/A |
2.936 |
|
|
\[ {}{y^{\prime }}^{2}-4 y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.335 |
|
|
\[ {}{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
90.18 |
|
|
\[ {}{y^{\prime }}^{2}-y^{2} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.23 |
|
|
\[ {}y^{\prime } = y^{\frac {2}{3}}+a \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.427 |
|
|
\[ {}\left (x y^{\prime }+y\right )^{2}+3 x^{5} \left (x y^{\prime }-2 y\right ) = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
69.164 |
|
|
\[ {}y \left (y-2 x y^{\prime }\right )^{2} = 2 y^{\prime } \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
3.633 |
|
|
\[ {}8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2} = 27 y-27 x \] |
dAlembert |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.437 |
|
|
\[ {}\left (y^{\prime }-1\right )^{2} = y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.35 |
|
|
\[ {}y = {y^{\prime }}^{2}-x y^{\prime }+x \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.348 |
|
|
\[ {}\left (x y^{\prime }+y\right )^{2} = y^{2} y^{\prime } \] |
dAlembert |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.498 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}+y^{2} = 1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.394 |
|
|
\[ {}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
3.18 |
|
|
\[ {}3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.298 |
|
|
\[ {}y = x y^{\prime }+\sqrt {a^{2} {y^{\prime }}^{2}+b^{2}} \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
2.647 |
|
|
\[ {}y^{\prime } = \left (x -y\right )^{2}+1 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.559 |
|
|
\[ {}x \sin \left (x \right ) y^{\prime }+\left (\sin \left (x \right )-x \cos \left (x \right )\right ) y = \sin \left (x \right ) \cos \left (x \right )-x \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
5.52 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = y^{n} \sin \left (2 x \right ) \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
9.935 |
|
|
\[ {}x^{3}-3 x y^{2}+\left (y^{3}-3 x^{2} y\right ) y^{\prime } = 0 \] |
exact, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
1.65 |
|
|
\[ {}5 x y-4 y^{2}-6 x^{2}+\left (y^{2}-8 x y+\frac {5 x^{2}}{2}\right ) y^{\prime } = 0 \] |
exact, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
1.411 |
|
|
\[ {}3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime } = 0 \] |
exact |
[_exact, _rational] |
✓ |
✓ |
1.541 |
|
|
\[ {}y-x y^{2} \ln \left (x \right )+x y^{\prime } = 0 \] |
riccati, bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
0.984 |
|
|
\[ {}2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime } = 0 \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.996 |
|
|
\[ {}y^{\prime } = \frac {1}{2 x -y^{2}} \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
0.829 |
|
|
\[ {}x^{2}+x y^{\prime } = 3 x +y^{\prime } \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.163 |
|
|
\[ {}x y y^{\prime }-y^{2} = x^{4} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.998 |
|
|
\[ {}\frac {1}{y^{2}-x y+x^{2}} = \frac {y^{\prime }}{2 y^{2}-x y} \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
16.427 |
|
|
\[ {}\left (2 x -1\right ) y^{\prime }-2 y = \frac {1-4 x}{x^{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.589 |
|
|
\[ {}x -y+3+\left (3 x +y+1\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.276 |
|
|
\[ {}y^{\prime }+\cos \left (\frac {x}{2}+\frac {y}{2}\right ) = \cos \left (\frac {x}{2}-\frac {y}{2}\right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.551 |
|
|
\[ {}y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right ) = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.583 |
|
|
\[ {}x y^{2} y^{\prime }-y^{3} = \frac {x^{4}}{3} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.174 |
|
|
\[ {}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0 \] |
exact, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
7.802 |
|
|
\[ {}x^{2}+y^{2}-x y y^{\prime } = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.013 |
|
|
\[ {}x -y+2+\left (x -y+3\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.623 |
|
|
\[ {}x y^{2}+y-x y^{\prime } = 0 \] |
riccati, bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.939 |
|
|
\[ {}x^{2}+y^{2}+2 x +2 y y^{\prime } = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.345 |
|
|
\[ {}\left (-1+x \right ) \left (y^{2}-y+1\right ) = \left (y-1\right ) \left (x^{2}+x +1\right ) y^{\prime } \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.444 |
|
|
\[ {}\left (x -2 x y-y^{2}\right ) y^{\prime }+y^{2} = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.728 |
|
|
\[ {}y \cos \left (x \right )+\left (2 y-\sin \left (x \right )\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.917 |
|
|
\[ {}y^{\prime }-1 = {\mathrm e}^{2 y+x} \] |
first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.79 |
|
|
\[ {}2 x^{5}+4 x^{3} y-2 x y^{2}+\left (y^{2}+2 x^{2} y-x^{4}\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.443 |
|
|
\[ {}x^{2} y^{n} y^{\prime } = 2 x y^{\prime }-y \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.296 |
|
|
\[ {}\left (3 x +3 y+a^{2}\right ) y^{\prime } = 4 x +4 y+b^{2} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.179 |
|
|
\[ {}x -y^{2}+2 x y y^{\prime } = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.971 |
|
|
\[ {}x y^{\prime }+y = y^{2} \ln \left (x \right ) \] |
riccati, bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
1.35 |
|
|
\[ {}\sin \left (\ln \left (x \right )\right )-\cos \left (\ln \left (y\right )\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
59.475 |
|
|
\[ {}y^{\prime } = \sqrt {\frac {9 y^{2}-6 y+2}{x^{2}-2 x +5}} \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
2.1 |
|
|
\[ {}\left (5 x -7 y+1\right ) y^{\prime }+x +y-1 = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.893 |
|
|
\[ {}x +y+1+\left (2 x +2 y-1\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.923 |
|
|
\[ {}y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime } = 0 \] |
exactByInspection, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.227 |
|
|
\[ {}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
1.625 |
|
|
\[ {}4 x^{2} {y^{\prime }}^{2}-y^{2} = x y^{3} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
45.149 |
|
|
\[ {}y^{\prime }+{y^{\prime }}^{2} x -y = 0 \] |
dAlembert |
[_rational, _dAlembert] |
✓ |
✓ |
0.367 |
|
|
\[ {}y^{\prime \prime }+y = 2 \cos \left (x \right )+2 \sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.612 |
|
|
\[ {}x y^{\prime \prime \prime } = 2 \] |
higher_order_missing_y |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
0.227 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{2} \] |
second_order_ode_missing_x, second_order_ode_missing_y |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.329 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime } = 1 \] |
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]] |
✓ |
✓ |
1.053 |
|
|
\[ {}{y^{\prime }}^{4} = 1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.375 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.675 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 2 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.315 |
|
|
\[ {}y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{\frac {3}{2}} \] |
second_order_ode_missing_x, second_order_ode_missing_y |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.97 |
|
|
\[ {}{y^{\prime }}^{2}+y y^{\prime \prime } = 1 \] |
second_order_integrable_as_is, second_order_ode_missing_x, exact nonlinear second order ode |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
6.869 |
|
|
\[ {}y^{\prime \prime \prime \prime } = x \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _quadrature]] |
✓ |
✓ |
0.132 |
|
|
\[ {}y^{\prime \prime \prime } = x +\cos \left (x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
0.182 |
|
|
\[ {}y^{\prime \prime } \left (2+x \right )^{5} = 1 \] |
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]] |
✓ |
✓ |
0.948 |
|
|
\[ {}y^{\prime \prime } = x \,{\mathrm e}^{x} \] |
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]] |
✓ |
✓ |
1.001 |
|
|
\[ {}y^{\prime \prime } = 2 x \ln \left (x \right ) \] |
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]] |
✓ |
✓ |
0.646 |
|
|
\[ {}x y^{\prime \prime } = y^{\prime } \] |
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]] |
✓ |
✓ |
1.02 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 0 \] |
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]] |
✓ |
✓ |
0.675 |
|
|
\[ {}x y^{\prime \prime } = \left (2 x^{2}+1\right ) y^{\prime } \] |
kovacic, second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.651 |
|
|
\[ {}x y^{\prime \prime } = y^{\prime }+x^{2} \] |
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]] |
✓ |
✓ |
1.184 |
|
|
\[ {}x \ln \left (x \right ) y^{\prime \prime } = y^{\prime } \] |
second_order_ode_missing_y, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.678 |
|
|
\[ {}x y = y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right ) \] |
separable |
[_separable] |
✓ |
✓ |
1.428 |
|
|
\[ {}2 y^{\prime \prime } = \frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }} \] |
second_order_ode_missing_y |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
0.941 |
|
|
\[ {}y^{\prime \prime \prime } = \sqrt {1-{y^{\prime \prime }}^{2}} \] |
unknown |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
❇ |
N/A |
0.0 |
|
|
\[ {}x y^{\prime \prime \prime }-y^{\prime \prime } = 0 \] |
higher_order_missing_y |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.553 |
|
|
\[ {}y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \] |
second_order_ode_missing_x, second_order_ode_missing_y |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.484 |
|
|
\[ {}y^{\prime \prime } = {y^{\prime }}^{2} \] |
second_order_ode_missing_x, second_order_ode_missing_y |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
0.346 |
|
|
\[ {}y^{\prime \prime } = \sqrt {1-{y^{\prime }}^{2}} \] |
second_order_ode_missing_x, second_order_ode_missing_y |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.649 |
|
|
|
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