|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime \prime }-12 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.283 |
|
|
\[
{}\left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.487 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = x \left (6-\ln \left (x \right )\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.887 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = \sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.319 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = -\frac {16 \ln \left (x \right )}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.770 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y = x^{2}-2 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.262 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.227 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 \ln \left (x \right )^{2}+12 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.687 |
|
|
\[
{}\left (x +1\right )^{3} y^{\prime \prime }+3 \left (x +1\right )^{2} y^{\prime }+\left (x +1\right ) y = 6 \ln \left (x +1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.645 |
|
|
\[
{}\left (-2+x \right )^{2} y^{\prime \prime }-3 \left (-2+x \right ) y^{\prime }+4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.584 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.141 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y = 0
\] |
[_Jacobi] |
✓ |
1.333 |
|
|
\[
{}\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (x +1\right ) y^{\prime }+6 y = 6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.578 |
|
|
\[
{}x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.332 |
|
|
\[
{}y^{\prime \prime }+\left (\tan \left (x \right )-2 \cot \left (x \right )\right ) y^{\prime }+2 \cot \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.383 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.415 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = 1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.411 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 5 x^{4}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.394 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = \left (x -1\right )^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.447 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-2 x} y = {\mathrm e}^{-3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.595 |
|
|
\[
{}\left (x^{4}-x^{3}\right ) y^{\prime \prime }+\left (2 x^{3}-2 x^{2}-x \right ) y^{\prime }-y = \frac {\left (x -1\right )^{2}}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.452 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y = x \,{\mathrm e}^{2 x}-1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.747 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y = x^{2} \left (2 x -3\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.434 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.681 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \frac {1}{1+{\mathrm e}^{x}}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.678 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\cos \left (x \right )^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.002 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.925 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.916 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{\sin \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.671 |
|
|
\[
{}y^{\prime \prime }+y = \frac {2}{\sin \left (x \right )^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.952 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.508 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = \frac {x -1}{x^{3}}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.245 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime } = 4 x^{3} {\mathrm e}^{x^{2}}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.201 |
|
|
\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime } = 1
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.314 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime \prime }-y^{\prime } = \ln \left (x \right )^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.011 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x -1\right ) y^{\prime } = -4 x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.184 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \cos \left (x \right ) \cot \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.316 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.744 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = \frac {6+x}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
52.590 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {1}{x^{2}+1}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.716 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (x -1\right )^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.807 |
|
|
\[
{}2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y = \frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.914 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y = 4 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.707 |
|
|
\[
{}x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x^{2} y^{\prime }+x y = 2 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.734 |
|
|
\[
{}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y = 2 x -2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.509 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.174 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+6 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.878 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.857 |
|
|
\[
{}x^{\prime \prime }+{x^{\prime }}^{2}+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.894 |
|
|
\[
{}x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.497 |
|
|
\[
{}x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.594 |
|
|
\[
{}x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.839 |
|
|
\[
{}x^{\prime \prime }+x {x^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.468 |
|
|
\[
{}x^{\prime \prime }+\left (x+2\right ) x^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.608 |
|
|
\[
{}x^{\prime \prime }-x^{\prime }+x-x^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.504 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.724 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.615 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.461 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.480 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.075 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.827 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.372 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.323 |
|
|
\[
{}y^{\prime \prime }+\alpha y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.721 |
|
|
\[
{}y^{\prime \prime }+\alpha ^{2} y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
6.934 |
|
|
\[
{}y^{\prime \prime }+y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.987 |
|
|
\[
{}y^{\prime \prime }+\lambda ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.867 |
|
|
\[
{}y^{\prime \prime }+\lambda ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.730 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.163 |
|
|
\[
{}y^{\prime \prime \prime \prime }-\lambda ^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.172 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.909 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.216 |
|
|
\[
{}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime } = 0
\] |
[[_high_order, _missing_y]] |
✓ |
0.244 |
|
|
\[
{}y^{\prime } = 1-x y
\] |
[_linear] |
✓ |
0.562 |
|
|
\[
{}y^{\prime } = \frac {y-x}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
0.252 |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
0.718 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.480 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } \sin \left (x \right ) = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.700 |
|
|
\[
{}x y^{\prime \prime }+y \sin \left (x \right ) = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.988 |
|
|
\[
{}\ln \left (x \right ) y^{\prime \prime }-y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
35.693 |
|
|
\[
{}y^{\prime \prime \prime }+x \sin \left (y\right ) = 0
\] |
[NONE] |
✗ |
0.007 |
|
|
\[
{}y^{\prime }-2 x y = 0
\] |
[_separable] |
✓ |
0.557 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.518 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.517 |
|
|
\[
{}y^{\prime \prime }-\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.519 |
|
|
\[
{}y^{\prime \prime } = x^{2} y-y^{\prime }
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.543 |
|
|
\[
{}y^{\prime \prime }-y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.655 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{y}+x y
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.336 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.893 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-n y = 0
\] |
[_separable] |
✓ |
0.585 |
|
|
\[
{}9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
[_Jacobi] |
✓ |
0.899 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-\frac {1}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.131 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.836 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{9} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.940 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.921 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }+4 \left (x^{4}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.385 |
|
|
\[
{}x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.370 |
|
|
\[
{}y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
0.973 |
|
|
\[
{}y^{\prime \prime }+\frac {3 y^{\prime }}{x}+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.956 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.008 |
|