|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.654 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.609 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.611 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.592 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.609 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.911 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.885 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.440 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.779 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.740 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.811 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.849 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.863 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.397 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.107 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.691 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1-2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.730 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.732 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.621 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.671 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (3 x +1\right ) y^{\prime }+\left (1-6 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.763 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (-1+x \right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.731 |
|
|
\[
{}x \left (-2+x \right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.700 |
|
|
\[
{}x \left (-2+x \right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.727 |
|
|
\[
{}4 \left (x -4\right )^{2} y^{\prime \prime }+\left (x -4\right ) \left (x -8\right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.781 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.734 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.480 |
|
|
\[
{}x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.534 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }+\left (3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.815 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.801 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x \left (x +1\right ) y^{\prime }+\left (1-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.778 |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.645 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x \left (-2+x \right ) y^{\prime }+2 \left (2-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.836 |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+2 x \left (1+6 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.924 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.830 |
|
|
\[
{}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
0.809 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.888 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.877 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.842 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.750 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.861 |
|
|
\[
{}x y^{\prime \prime }+\left (3 x +4\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.780 |
|
|
\[
{}x y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.842 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.801 |
|
|
\[
{}x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.778 |
|
|
\[
{}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.860 |
|
|
\[
{}x y^{\prime \prime }+\left (x^{3}-1\right ) y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.646 |
|
|
\[
{}x^{2} \left (4 x -1\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.985 |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.177 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.401 |
|
|
\[
{}2 x y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.298 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x \left (2-x \right ) y^{\prime }-\left (3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.437 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.452 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.382 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
1.366 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
1.400 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
0.701 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.241 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (8+5 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.410 |
|
|
\[
{}x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-5 y = 0
\] |
[_Laguerre] |
✓ |
1.394 |
|
|
\[
{}9 x^{2} y^{\prime \prime }-15 x y^{\prime }+7 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.457 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.475 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x^{3}+x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.829 |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[_Jacobi] |
✓ |
1.000 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.663 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (6 x^{2}-3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.911 |
|
|
\[
{}x y^{\prime \prime }+x y^{\prime }+\left (x^{4}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.415 |
|
|
\[
{}x \left (-2+x \right )^{2} y^{\prime \prime }-2 \left (-2+x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.825 |
|
|
\[
{}x \left (-2+x \right )^{2} y^{\prime \prime }-2 \left (-2+x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.724 |
|
|
\[
{}2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.882 |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.378 |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }-2 y = 0
\] |
[_Laguerre] |
✓ |
1.409 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.862 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +7\right ) y^{\prime }+2 \left (x +5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.867 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.798 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }-18 y = 0
\] |
[_Gegenbauer] |
✓ |
0.533 |
|
|
\[
{}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.864 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }-8 y = 0
\] |
[_erf] |
✓ |
0.379 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime \prime }-\left (x^{2}+7\right ) y^{\prime }+4 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.776 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.929 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.898 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.662 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.826 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}-3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.646 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.806 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.414 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.908 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+3 x^{2} y^{\prime }+\left (3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.838 |
|
|
\[
{}x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.611 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.877 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime \prime }+5 \left (-x^{2}+1\right ) y^{\prime }-4 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.721 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.744 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+4\right ) y = 0
\] |
[[_Bessel, _modified]] |
✓ |
1.330 |
|
|
\[
{}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+18 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.898 |
|
|
\[
{}x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.774 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.750 |
|
|
\[
{}y^{\prime } = \frac {y}{\ln \left (x \right ) x}
\] |
[_separable] |
✓ |
1.545 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
2.938 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 5 x^{2}
\] |
[_linear] |
✓ |
1.684 |
|
|
\[
{}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
1.371 |
|