|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.395 |
|
|
\[
{}y^{\prime \prime }+\left (1+4 i\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.551 |
|
|
\[
{}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.832 |
|
|
\[
{}y^{\prime \prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.885 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.656 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.605 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.994 |
|
|
\[
{}y^{\prime \prime }+2 i y^{\prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.775 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x}+2 x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
13.131 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.374 |
|
|
\[
{}y^{\prime \prime }+y = 2 \sin \left (x \right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.372 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.704 |
|
|
\[
{}4 y^{\prime \prime }-y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.998 |
|
|
\[
{}6 y^{\prime \prime }+5 y^{\prime }-6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.757 |
|
|
\[
{}y^{\prime \prime }+\omega ^{2} y = A \cos \left (\omega x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.036 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }+6 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.063 |
|
|
\[
{}y^{\prime \prime \prime }-i y^{\prime \prime }+4 y^{\prime }-4 i y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.092 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.075 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}y^{\prime \prime \prime }-3 i y^{\prime \prime }-3 y^{\prime }+i y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.090 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.132 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime }-y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.096 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.840 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.915 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.073 |
|
|
\[
{}y^{\left (5\right )}+2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.152 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}y^{\prime \prime \prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.148 |
|
|
\[
{}y^{\prime \prime \prime }-i y^{\prime \prime }+y^{\prime }-i y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.090 |
|
|
\[
{}y^{\prime \prime }-2 i y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.635 |
|
|
\[
{}y^{\prime \prime \prime \prime }-k^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.173 |
|
|
\[
{}y^{\prime \prime \prime }-y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.114 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = {\mathrm e}^{i x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.500 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.150 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.136 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.773 |
|
|
\[
{}y^{\prime \prime }-2 i y^{\prime }-y = {\mathrm e}^{i x}-2 \,{\mathrm e}^{-i x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.401 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.605 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.624 |
|
|
\[
{}y^{\prime \prime }-4 y = 3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.302 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = x^{2}+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.671 |
|
|
\[
{}y^{\prime \prime }+9 y = x^{2} {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.683 |
|
|
\[
{}y^{\prime \prime }+y = x \,{\mathrm e}^{x} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.383 |
|
|
\[
{}y^{\prime \prime }+i y^{\prime }+2 y = 2 \cosh \left (2 x \right )+{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.337 |
|
|
\[
{}y^{\prime \prime \prime } = x^{2}+{\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.596 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = x^{2} {\mathrm e}^{-x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.141 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
2.168 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.871 |
|
|
\[
{}\left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.382 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.318 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.322 |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
0.333 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.341 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.334 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.127 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.313 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.318 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.842 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[_Hermite] |
✓ |
0.487 |
|
|
\[
{}y^{\prime \prime }+3 x^{2} y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.555 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.458 |
|
|
\[
{}y^{\prime \prime }+x^{3} y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.559 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.306 |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right )^{2} y^{\prime }-\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.540 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.584 |
|
|
\[
{}y^{\prime \prime }+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.625 |
|
|
\[
{}y^{\prime \prime \prime }-x y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.047 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\alpha \left (1+\alpha \right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.721 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\alpha ^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.613 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+2 \alpha y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.604 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.026 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.182 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.019 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.615 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
0.124 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.310 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.026 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-2-i\right ) x y^{\prime }+3 i y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.329 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 \pi y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.883 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.073 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+x^{6} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.362 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.161 |
|
|
\[
{}x y^{\prime \prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.244 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.913 |
|
|
\[
{}\left (x^{2}+x -2\right )^{2} y^{\prime \prime }+3 \left (x +2\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.421 |
|
|
\[
{}x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.917 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.977 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (4 x^{4}-5 x \right ) y^{\prime }+\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.088 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-3 x^{2}+x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.977 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+5 x y^{\prime }+3 x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.038 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0
\] |
[_Lienard] |
✓ |
0.732 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \,{\mathrm e}^{x} y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.050 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+\left (x^{2}+5 x \right ) y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.183 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x \,{\mathrm e}^{x} y^{\prime }+3 y \cos \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.980 |
|
|
\[
{}\left (-x^{2}+1\right ) x^{2} y^{\prime \prime }+3 \left (x^{2}+x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.056 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.933 |
|