|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+y^{\prime }+y+1 = \sin \left (x \right )+x +x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
78.276 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.826 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+1 = 3 \sin \left (2 x \right )+\cos \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
4.052 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = 2 x +{\mathrm e}^{x}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime }+y = 2 \sin \left (x \right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.842 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = 4 x +3 \sin \left (x \right )+\cos \left (x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.161 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = x \,{\mathrm e}^{2 x}+\sin \left (x \right )+x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
1.328 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime } = x \,{\mathrm e}^{x}-1
\] |
[[_high_order, _missing_y]] |
✓ |
0.143 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime } = x +2 \,{\mathrm e}^{-x}
\] |
[[_high_order, _missing_y]] |
✓ |
0.138 |
|
|
\[
{}y^{\prime \prime }+y = -2 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.076 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 9 x^{2}-12 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.519 |
|
|
\[
{}y^{\prime \prime }+9 y = 36 \,{\mathrm e}^{3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.056 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.008 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = \left (12 x -7\right ) {\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.339 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.680 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.574 |
|
|
\[
{}y^{\prime \prime }+y = 2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.391 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.196 |
|
|
\[
{}y^{\prime \prime }+y = 4 x \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.740 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 2 x^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.487 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 16 \,{\mathrm e}^{-x}+9 x -6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.727 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = -5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.512 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.739 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime } = -2 x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.152 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 8 \,{\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime \prime }-y = 2 x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.163 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 8 \,{\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.189 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
14.434 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \cos \left (2 x \right )+\sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
23.828 |
|
|
\[
{}y^{\prime \prime }-y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.102 |
|
|
\[
{}y^{\prime \prime }-y = -2 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.395 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.068 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 8 \,{\mathrm e}^{x}+9
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.933 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-5 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.757 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
2.610 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.023 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.450 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.184 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.026 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.570 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.707 |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime \prime }+3 \left (x +2\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.845 |
|
|
\[
{}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.882 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.170 |
|
|
\[
{}x^{2} y^{\prime \prime \prime } = 2 y^{\prime }
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.162 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime \prime }-12 y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.257 |
|
|
\[
{}\left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } = 0
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.418 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = x \left (6-\ln \left (x \right )\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.579 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = \sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.973 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = -\frac {16 \ln \left (x \right )}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.453 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y = x^{2}-2 x +2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.854 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.119 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 2 \ln \left (x \right )^{2}+12 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.375 |
|
|
\[
{}\left (x +1\right )^{3} y^{\prime \prime }+3 \left (x +1\right )^{2} y^{\prime }+\left (x +1\right ) y = 6 \ln \left (x +1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.442 |
|
|
\[
{}\left (-2+x \right )^{2} y^{\prime \prime }-3 \left (-2+x \right ) y^{\prime }+4 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.204 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.928 |
|
|
\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y = 0
\] |
[_Jacobi] |
✓ |
1.208 |
|
|
\[
{}\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (x +1\right ) y^{\prime }+6 y = 6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.424 |
|
|
\[
{}x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.089 |
|
|
\[
{}y^{\prime \prime }+\left (\tan \left (x \right )-2 \cot \left (x \right )\right ) y^{\prime }+2 \cot \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.149 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.175 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y = 1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.169 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 5 x^{4}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.161 |
|
|
\[
{}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = \left (-1+x \right )^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.208 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+{\mathrm e}^{-2 x} y = {\mathrm e}^{-3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.405 |
|
|
\[
{}\left (x^{4}-x^{3}\right ) y^{\prime \prime }+\left (2 x^{3}-2 x^{2}-x \right ) y^{\prime }-y = \frac {\left (-1+x \right )^{2}}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.214 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y = x \,{\mathrm e}^{2 x}-1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.446 |
|
|
\[
{}x \left (-1+x \right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y = x^{2} \left (2 x -3\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.209 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\sin \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.678 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = \frac {1}{{\mathrm e}^{x}+1}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.088 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\cos \left (x \right )^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.959 |
|
|
\[
{}y^{\prime \prime }+y = \frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.978 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.742 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \frac {{\mathrm e}^{-x}}{\sin \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
30.145 |
|
|
\[
{}y^{\prime \prime }+y = \frac {2}{\sin \left (x \right )^{3}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.877 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.071 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = \frac {-1+x}{x^{3}}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.209 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime } = 4 x^{3} {\mathrm e}^{x^{2}}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.966 |
|
|
\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime } = 1
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.128 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime \prime }-y^{\prime } = \ln \left (x \right )^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.876 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x -1\right ) y^{\prime } = -4 x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.976 |
|
|
\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \cos \left (x \right ) \cot \left (x \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.243 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.589 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = \frac {6+x}{x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
147.653 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {1}{x^{2}+1}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.650 |
|
|
\[
{}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (-1+x \right )^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.661 |
|
|
\[
{}2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y = \frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.989 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y = 4 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.820 |
|
|
\[
{}x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x^{2} y^{\prime }+x y = 2 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.862 |
|
|
\[
{}\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y = 2 x -2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.459 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.247 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+6 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.022 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.974 |
|
|
\[
{}x^{\prime \prime }+{x^{\prime }}^{2}+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.114 |
|
|
\[
{}x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.691 |
|
|
\[
{}x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.734 |
|
|
\[
{}x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
3.037 |
|
|
\[
{}x^{\prime \prime }+x {x^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.358 |
|
|
\[
{}x^{\prime \prime }+\left (x+2\right ) x^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.217 |
|
|
\[
{}x^{\prime \prime }-x^{\prime }+x-x^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.743 |
|