|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
1.460 |
|
|
\[
{}y^{\prime } x +y = 3 x^{3}-1
\] |
[_linear] |
✓ |
1.242 |
|
|
\[
{}y^{\prime }+y \,{\mathrm e}^{x} = 3 \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
1.646 |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = {\mathrm e}^{\sin \left (x \right )}
\] |
[_linear] |
✓ |
1.852 |
|
|
\[
{}y^{\prime }+2 x y = x \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
2.515 |
|
|
\[
{}y^{\prime }+\cos \left (x \right ) y = {\mathrm e}^{-\sin \left (x \right )}
\] |
[_linear] |
✓ |
1.964 |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 1
\] |
[_linear] |
✓ |
1.473 |
|
|
\[
{}y^{\prime }+2 y = b \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.171 |
|
|
\[
{}y^{\prime } = 1+y
\] |
[_quadrature] |
✓ |
1.370 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
1.473 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
1.483 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.415 |
|
|
\[
{}3 y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.431 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.375 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.063 |
|
|
\[
{}y^{\prime \prime }+2 i y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.135 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.559 |
|
|
\[
{}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.820 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.715 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.707 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.988 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.579 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.626 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.690 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.694 |
|
|
\[
{}y^{\prime \prime }+\left (1+4 i\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.918 |
|
|
\[
{}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.933 |
|
|
\[
{}y^{\prime \prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.232 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.969 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.975 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.288 |
|
|
\[
{}y^{\prime \prime }+2 i y^{\prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.867 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x}+2 x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
14.473 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.657 |
|
|
\[
{}y^{\prime \prime }+y = 2 \sin \left (x \right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.677 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.051 |
|
|
\[
{}4 y^{\prime \prime }-y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.309 |
|
|
\[
{}6 y^{\prime \prime }+5 y^{\prime }-6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.036 |
|
|
\[
{}y^{\prime \prime }+\omega ^{2} y = A \cos \left (\omega x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.976 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.098 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }+6 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}y^{\prime \prime \prime }-i y^{\prime \prime }+4 y^{\prime }-4 i y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.102 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.089 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}y^{\prime \prime \prime }-3 i y^{\prime \prime }-3 y^{\prime }+i y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.100 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.139 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime }-y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.109 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.241 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.257 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y^{\left (5\right )}+2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.159 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime \prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.161 |
|
|
\[
{}y^{\prime \prime \prime }-i y^{\prime \prime }+y^{\prime }-i y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.104 |
|
|
\[
{}y^{\prime \prime }-2 i y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.652 |
|
|
\[
{}y^{\prime \prime \prime \prime }-k^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.202 |
|
|
\[
{}y^{\prime \prime \prime }-y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.114 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = {\mathrm e}^{i x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.505 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.153 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.140 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.528 |
|
|
\[
{}y^{\prime \prime }-2 i y^{\prime }-y = {\mathrm e}^{i x}-2 \,{\mathrm e}^{-i x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.467 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.904 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.927 |
|
|
\[
{}y^{\prime \prime }-4 y = 3 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.623 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = x^{2}+\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.896 |
|
|
\[
{}y^{\prime \prime }+9 y = x^{2} {\mathrm e}^{3 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.987 |
|
|
\[
{}y^{\prime \prime }+y = x \,{\mathrm e}^{x} \cos \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.770 |
|
|
\[
{}y^{\prime \prime }+i y^{\prime }+2 y = 2 \cosh \left (2 x \right )+{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.397 |
|
|
\[
{}y^{\prime \prime \prime } = x^{2}+{\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.625 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = x^{2} {\mathrm e}^{-x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.158 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
2.213 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.896 |
|
|
\[
{}\left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.437 |
|
|
\[
{}x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.321 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.322 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.335 |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
0.345 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.347 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.340 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.128 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.317 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.324 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.702 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[_Hermite] |
✓ |
0.492 |
|
|
\[
{}y^{\prime \prime }+3 x^{2} y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.526 |
|
|
\[
{}y^{\prime \prime }-x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.472 |
|
|
\[
{}y^{\prime \prime }+x^{3} y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.574 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.398 |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right )^{2} y^{\prime }-\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.544 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.594 |
|
|
\[
{}y^{\prime \prime }+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.628 |
|
|
\[
{}y^{\prime \prime \prime }-x y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.060 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\alpha \left (\alpha +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.752 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\alpha ^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.644 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 \alpha y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.630 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.042 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.200 |
|