|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.180 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (-x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.230 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.257 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.899 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.299 |
|
|
\[
{}\left (2 x^{3}-1\right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.546 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.625 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 n x \left (x +1\right ) y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.003 |
|
|
\[
{}x^{4} y^{\prime \prime }+2 x^{3} \left (x +1\right ) y^{\prime }+n^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.685 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.680 |
|
|
\[
{}\left (x y^{\prime \prime \prime }-y^{\prime \prime }\right )^{2} = {y^{\prime \prime \prime }}^{2}+1
\] |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] |
✓ |
1.018 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x = x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.286 |
|
|
\[
{}y^{\prime \prime } = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.173 |
|
|
\[
{}\left (y^{\prime }-x y^{\prime \prime }\right )^{2} = 1+{y^{\prime \prime }}^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.627 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-y^{2} y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.389 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.044 |
|
|
\[
{}2 y^{\prime \prime } = {\mathrm e}^{y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
34.146 |
|
|
\[
{}y^{\prime \prime } y+2 y^{\prime }-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.257 |
|
|
\[
{}\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.055 |
|
|
\[
{}x y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime } x +y = -x^{2}+1
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.058 |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime \prime \prime }+\left (x +2\right ) y^{\prime \prime }+y^{\prime } = 1
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.838 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +y = x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.554 |
|
|
\[
{}\left (x -1\right )^{2} y^{\prime \prime }+4 \left (x -1\right ) y^{\prime }+2 y = \cos \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.733 |
|
|
\[
{}\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 y^{\prime } x +4 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✗ |
0.056 |
|
|
\[
{}2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 x^{2} {y^{\prime }}^{2}+36 x y y^{\prime }+6 y^{2} = 0
\] |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.050 |
|
|
\[
{}x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.257 |
|
|
\[
{}x^{2} \left (-x^{3}+1\right ) y^{\prime \prime }-x^{3} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
112.836 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.043 |
|
|
\[
{}y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }+2 \tan \left (x \right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.082 |
|
|
\[
{}x^{2} y y^{\prime \prime }+\left (-y+y^{\prime } x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.084 |
|
|
\[
{}x^{3} y^{\prime \prime }-\left (-y+y^{\prime } x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.087 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )-x^{2} y^{2}
\] |
[[_2nd_order, _reducible, _mu_xy]] |
✗ |
0.161 |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.441 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.361 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x = 2
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.319 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.537 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+18 y^{\prime } x +6 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✗ |
0.049 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (4 x +2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.361 |
|
|
\[
{}y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.456 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.766 |
|
|
\[
{}x \left (x +2 y\right ) y^{\prime \prime }+2 x {y^{\prime }}^{2}+4 \left (x +y\right ) y^{\prime }+2 y+x^{2} = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.856 |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.358 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
36.503 |
|
|
\[
{}4 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.247 |
|
|
\[
{}\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 \sin \left (x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.992 |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }+3 x+2 y={\mathrm e}^{t} \\ 4 x-3 y^{\prime }+3 y=3 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.549 |
|
|
\[
{}x^{\prime } = \frac {2 x}{t}
\] |
[_separable] |
✓ |
1.425 |
|
|
\[
{}x^{\prime } = -\frac {t}{x}
\] |
[_separable] |
✓ |
2.618 |
|
|
\[
{}x^{\prime } = -x^{2}
\] |
[_quadrature] |
✓ |
0.404 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.194 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{-x}
\] |
[_quadrature] |
✓ |
0.396 |
|
|
\[
{}x^{\prime }+2 x = t^{2}+4 t +7
\] |
[[_linear, ‘class A‘]] |
✓ |
0.954 |
|
|
\[
{}2 t x^{\prime } = x
\] |
[_separable] |
✓ |
1.438 |
|
|
\[
{}t^{2} x^{\prime \prime }-6 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.627 |
|
|
\[
{}2 x^{\prime \prime }-5 x^{\prime }-3 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.776 |
|
|
\[
{}x^{\prime } = x \left (1-\frac {x}{4}\right )
\] |
[_quadrature] |
✓ |
0.725 |
|
|
\[
{}x^{\prime } = x^{2}+t^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.012 |
|
|
\[
{}x^{\prime } = t \cos \left (t^{2}\right )
\] |
[_quadrature] |
✓ |
0.524 |
|
|
\[
{}x^{\prime } = \frac {1+t}{\sqrt {t}}
\] |
[_quadrature] |
✓ |
0.461 |
|
|
\[
{}x^{\prime \prime } = -3 \sqrt {t}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.600 |
|
|
\[
{}x^{\prime } = t \,{\mathrm e}^{-2 t}
\] |
[_quadrature] |
✓ |
0.281 |
|
|
\[
{}x^{\prime } = \frac {1}{t \ln \left (t \right )}
\] |
[_quadrature] |
✓ |
0.262 |
|
|
\[
{}\sqrt {t}\, x^{\prime } = \cos \left (\sqrt {t}\right )
\] |
[_quadrature] |
✓ |
0.377 |
|
|
\[
{}x^{\prime } = \frac {{\mathrm e}^{-t}}{\sqrt {t}}
\] |
[_quadrature] |
✓ |
0.529 |
|
|
\[
{}x^{\prime }+t x^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.470 |
|
|
\[
{}x^{\prime } = \sqrt {x}
\] |
[_quadrature] |
✓ |
0.674 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{-2 x}
\] |
[_quadrature] |
✓ |
0.704 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.405 |
|
|
\[
{}u^{\prime } = \frac {1}{5-2 u}
\] |
[_quadrature] |
✓ |
0.471 |
|
|
\[
{}x^{\prime } = a x+b
\] |
[_quadrature] |
✓ |
0.323 |
|
|
\[
{}Q^{\prime } = \frac {Q}{4+Q^{2}}
\] |
[_quadrature] |
✓ |
0.478 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{x^{2}}
\] |
[_quadrature] |
✓ |
0.401 |
|
|
\[
{}y^{\prime } = r \left (a -y\right )
\] |
[_quadrature] |
✓ |
0.368 |
|
|
\[
{}x^{\prime } = \frac {2 x}{1+t}
\] |
[_separable] |
✓ |
1.398 |
|
|
\[
{}\theta ^{\prime } = t \sqrt {t^{2}+1}\, \sec \left (\theta \right )
\] |
[_separable] |
✓ |
1.765 |
|
|
\[
{}\left (2 u+1\right ) u^{\prime }-1-t = 0
\] |
[_separable] |
✓ |
2.359 |
|
|
\[
{}R^{\prime } = \left (1+t \right ) \left (1+R^{2}\right )
\] |
[_separable] |
✓ |
1.878 |
|
|
\[
{}y^{\prime }+y+\frac {1}{y} = 0
\] |
[_quadrature] |
✓ |
5.415 |
|
|
\[
{}\left (1+t \right ) x^{\prime }+x^{2} = 0
\] |
[_separable] |
✓ |
1.330 |
|
|
\[
{}y^{\prime } = \frac {1}{2 y+1}
\] |
[_quadrature] |
✓ |
0.352 |
|
|
\[
{}x^{\prime } = \left (4 t -x\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.956 |
|
|
\[
{}x^{\prime } = 2 t x^{2}
\] |
[_separable] |
✓ |
1.828 |
|
|
\[
{}x^{\prime } = t^{2} {\mathrm e}^{-x}
\] |
[_separable] |
✓ |
2.717 |
|
|
\[
{}x^{\prime } = x \left (4+x\right )
\] |
[_quadrature] |
✓ |
1.195 |
|
|
\[
{}x^{\prime } = {\mathrm e}^{t +x}
\] |
[_separable] |
✓ |
2.380 |
|
|
\[
{}T^{\prime } = 2 a t \left (T^{2}-a^{2}\right )
\] |
[_separable] |
✓ |
2.231 |
|
|
\[
{}y^{\prime } = t^{2} \tan \left (y\right )
\] |
[_separable] |
✓ |
1.711 |
|
|
\[
{}x^{\prime } = \frac {\left (4+2 t \right ) x}{\ln \left (x\right )}
\] |
[_separable] |
✓ |
1.454 |
|
|
\[
{}y^{\prime } = \frac {2 t y^{2}}{t^{2}+1}
\] |
[_separable] |
✓ |
1.932 |
|
|
\[
{}x^{\prime } = \frac {t^{2}}{1-x^{2}}
\] |
[_separable] |
✓ |
1.081 |
|
|
\[
{}x^{\prime } = 6 t \left (x-1\right )^{{2}/{3}}
\] |
[_separable] |
✓ |
1.648 |
|
|
\[
{}x^{\prime } = \frac {4 t^{2}+3 x^{2}}{2 x t}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.531 |
|
|
\[
{}x^{\prime } {\mathrm e}^{2 t}+2 x \,{\mathrm e}^{2 t} = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.367 |
|
|
\[
{}\frac {x^{\prime }+t x^{\prime \prime }}{t} = -2
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.964 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 t y}{t^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.938 |
|
|
\[
{}y^{\prime } = -y^{2} {\mathrm e}^{-t^{2}}
\] |
[_separable] |
✓ |
1.812 |
|
|
\[
{}x^{\prime } = 2 t^{3} x-6
\] |
[_linear] |
✓ |
1.276 |
|
|
\[
{}\cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right ) = 0
\] |
[_separable] |
✓ |
2.459 |
|
|
\[
{}x^{\prime } = t -x^{2}
\] |
[[_Riccati, _special]] |
✓ |
0.970 |
|
|
\[
{}7 t^{2} x^{\prime } = 3 x-2 t
\] |
[_linear] |
✓ |
1.024 |
|