|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (x^{2}-9\right ) y^{\prime \prime }+3 y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.592 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.592 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+6 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.653 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }-5 y^{\prime } x +3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.620 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.485 |
|
|
\[
{}\left (-4 x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x -4 y = 0
\] |
[_Gegenbauer] |
✓ |
0.623 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+3 y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.635 |
|
|
\[
{}y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✗ |
0.046 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +3 y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.685 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.591 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } x +7 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.590 |
|
|
\[
{}2 y^{\prime \prime }+9 y^{\prime } x -36 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.576 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.599 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+3 y^{\prime } x -8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.618 |
|
|
\[
{}\left (9 x^{2}+1\right ) y^{\prime \prime }-18 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.621 |
|
|
\[
{}\left (3 x^{2}+1\right ) y^{\prime \prime }+13 y^{\prime } x +7 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.641 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+11 y^{\prime } x +9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.646 |
|
|
\[
{}y^{\prime \prime }-2 \left (x +3\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.621 |
|
|
\[
{}y^{\prime \prime }+\left (x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.506 |
|
|
\[
{}\left (x^{2}-2 x +2\right ) y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.509 |
|
|
\[
{}2 x \left (x +1\right ) y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.960 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.882 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.871 |
|
|
\[
{}4 x y^{\prime \prime }+3 y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.000 |
|
|
\[
{}2 x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (1+7 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.014 |
|
|
\[
{}2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.045 |
|
|
\[
{}8 x^{2} y^{\prime \prime }+10 y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.058 |
|
|
\[
{}2 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.825 |
|
|
\[
{}2 x \left (x +3\right ) y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.982 |
|
|
\[
{}2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 y x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.806 |
|
|
\[
{}x \left (4-x \right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.075 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.135 |
|
|
\[
{}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.069 |
|
|
\[
{}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.115 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 x \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.082 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (4 x -1\right ) y^{\prime }+2 \left (3 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.076 |
|
|
\[
{}2 x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.887 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.784 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.830 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.772 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.817 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.967 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.013 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.629 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.098 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.979 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.160 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.098 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.983 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.721 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-8 y^{\prime } x +8 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.118 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.856 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1-2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.895 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.935 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.756 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.813 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (3 x +1\right ) y^{\prime }+\left (1-6 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.982 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.915 |
|
|
\[
{}x \left (x -2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.835 |
|
|
\[
{}x \left (x -2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.939 |
|
|
\[
{}4 \left (x -4\right )^{2} y^{\prime \prime }+\left (x -4\right ) \left (x -8\right ) y^{\prime }+y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.010 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.918 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.675 |
|
|
\[
{}x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-y x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.751 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }+\left (3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.067 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.981 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x \left (x +1\right ) y^{\prime }+\left (1-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.926 |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.925 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x \left (x -2\right ) y^{\prime }+2 \left (2-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.095 |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+2 x \left (1+6 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.086 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2+3 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.034 |
|
|
\[
{}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
0.990 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (5+x \right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.091 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (5+x \right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.042 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.110 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.933 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.036 |
|
|
\[
{}x y^{\prime \prime }+\left (4+3 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.012 |
|
|
\[
{}x y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.027 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.992 |
|
|
\[
{}x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.956 |
|
|
\[
{}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.042 |
|
|
\[
{}x y^{\prime \prime }+\left (x^{3}-1\right ) y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.794 |
|
|
\[
{}x^{2} \left (4 x -1\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.270 |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.155 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.342 |
|
|
\[
{}2 x y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.240 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x \left (2-x \right ) y^{\prime }-\left (3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.359 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.399 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.296 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
1.292 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
1.312 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
0.809 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.171 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +\left (8+5 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.321 |
|
|
\[
{}x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-5 y = 0
\] |
[_Laguerre] |
✓ |
1.319 |
|
|
\[
{}9 x^{2} y^{\prime \prime }-15 y^{\prime } x +7 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.446 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.440 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (x^{3}+x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.958 |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[_Jacobi] |
✓ |
1.144 |
|