|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-2 y^{\prime }-x y-x^{3}-x^{2} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.357 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.368 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.359 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.363 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.366 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.366 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{4}+3 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.368 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.275 |
|
|
\[
{}y^{\prime \prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.012 |
|
|
\[
{}y^{\prime \prime }-x y-x^{6}+64 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.501 |
|
|
\[
{}y^{\prime \prime }-x y-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.547 |
|
|
\[
{}y^{\prime \prime }-x y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.865 |
|
|
\[
{}y^{\prime \prime }-x y-x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.214 |
|
|
\[
{}y^{\prime \prime }-x y-x^{6}-x^{3}+42 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.288 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.935 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
63.403 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{4} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.930 |
|
|
\[
{}y^{\prime \prime }-x^{2} y-x^{4}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.122 |
|
|
\[
{}y^{\prime \prime }-2 x^{2} y-x^{4}+1 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.755 |
|
|
\[
{}y^{\prime \prime }-x^{3} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
15.593 |
|
|
\[
{}y^{\prime \prime }-x^{3} y-x^{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
297.633 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.677 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.578 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.985 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.845 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{2} y-x^{3}-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.685 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-x^{3} y-x^{4}-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.713 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-x y-x^{2}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
193.839 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.777 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{3} y-x^{4}-\frac {1}{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
421.055 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x y-x^{3}-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.579 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.791 |
|
|
\[
{}y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.584 |
|
|
\[
{}y^{\prime \prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.056 |
|
|
\[
{}y^{\prime \prime }+c y^{\prime }+k y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.092 |
|
|
\[
{}w^{\prime } = -\frac {1}{2}-\frac {\sqrt {1-12 w}}{2}
\] |
[_quadrature] |
✓ |
9.250 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.873 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.937 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.168 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.932 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.960 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.995 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.112 |
|
|
\[
{}y^{\prime \prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.929 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
44.620 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
41.816 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
49.402 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime }+y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.526 |
|
|
\[
{}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.713 |
|
|
\[
{}x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.662 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.388 |
|
|
\[
{}x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.182 |
|
|
\[
{}x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
3.385 |
|
|
\[
{}5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.286 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.725 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = x
\] |
[[_2nd_order, _missing_y]] |
✗ |
1121.960 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+x {y^{\prime }}^{2} = 1
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.763 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y {y^{\prime }}^{2} = 0
\] |
[NONE] |
✗ |
0.093 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.548 |
|
|
\[
{}y^{\prime \prime }+\sin \left (y\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.362 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
1.047 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.757 |
|
|
\[
{}y^{\prime } = 2 x^{2} \sin \left (\frac {y}{x}\right )^{2}+\frac {y}{x}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
3.070 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 8 \sqrt {x}\, \left (\ln \left (x \right )+1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.897 |
|
|
\[
{}v v^{\prime } = \frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3}
\] |
[_rational, _Bernoulli] |
✓ |
1.536 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.815 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.882 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.874 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.830 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}+x +1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.957 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.876 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.928 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.926 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.915 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \sin \left (x \right )+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.970 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.007 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \sin \left (x \right )+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.973 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (\cos \left (x \right )-1\right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.122 |
|
|
\[
{}\left (-2+x \right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.877 |
|
|
\[
{}\left (-2+x \right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.949 |
|
|
\[
{}\left (x +1\right ) \left (3 x -1\right ) y^{\prime \prime }+\cos \left (x \right ) y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.105 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.752 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-x y = x^{2}+2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.039 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.874 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+2 x y^{\prime }-x y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.763 |
|
|
\[
{}y^{\prime \prime }+\left (x -6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.517 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x^{2}+2 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.945 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{2}+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.064 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.048 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{3}+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.125 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.006 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = x^{3} \cos \left (x \right )+\sin \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.115 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (-x^{2}+1\right ) y = \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.800 |
|
|
\[
{}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.023 |
|
|
\[
{}x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.936 |
|
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.933 |
|
|
\[
{}{y^{\prime }}^{2}+y^{2} = \sec \left (x \right )^{4}
\] |
[‘y=_G(x,y’)‘] |
✓ |
33.003 |
|
|
\[
{}\left (y-2 x y^{\prime }\right )^{2} = {y^{\prime }}^{3}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✗ |
267.458 |
|
|
\[
{}x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.651 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.746 |
|