|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.426 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.471 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-5 y \\ y^{\prime }=-x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.649 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=-4 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.657 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y+z \\ y^{\prime }=-2 x-y+3 z \\ z^{\prime }=x+y+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.550 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+y-z \\ y^{\prime }=2 x-y-4 z \\ z^{\prime }=3 x-y+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
9.285 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y-4 t +1 \\ y^{\prime }=-x+2 y+3 t +4 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.355 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y-t +3 \\ y^{\prime }=x+4 y+t -2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.941 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y-t +3 \\ y^{\prime }=-x-5 y+t +1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.341 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x y+1 \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.067 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=t y+1 \\ y^{\prime }=-t x+y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.072 |
|
|
\[
{}y^{\prime } = y^{2}-x
\] |
[[_Riccati, _special]] |
✓ |
0.401 |
|
|
\[
{}y^{\prime } = y^{2}-x
\] |
[[_Riccati, _special]] |
✓ |
2.082 |
|
|
\[
{}y^{\prime }-2 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.752 |
|
|
\[
{}y^{\prime }-2 y = x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.664 |
|
|
\[
{}y^{\prime } = y+x \,{\mathrm e}^{y}
\] |
[‘y=_G(x,y’)‘] |
✓ |
0.735 |
|
|
\[
{}y^{\prime } = y+x \,{\mathrm e}^{y}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.077 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.434 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.301 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.652 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.354 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.641 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.835 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.685 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.033 |
|
|
\[
{}y^{\prime \prime }-x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.532 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.572 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +y = 0
\] |
[_Lienard] |
✓ |
0.654 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } x +2 y = 0
\] |
[_Hermite] |
✓ |
0.581 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.678 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.669 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.659 |
|
|
\[
{}\left (x +2\right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.658 |
|
|
\[
{}y^{\prime \prime }-\left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.733 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.691 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+3 y^{\prime } x -y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.744 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.681 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.566 |
|
|
\[
{}\left (x +1\right ) y^{\prime \prime }-\left (2-x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.739 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.628 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.668 |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.871 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.970 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.765 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
6.989 |
|
|
\[
{}y^{\prime \prime }-x y = 1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.574 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime } x -4 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
0.760 |
|
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.220 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } x +\sqrt {x}\, y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.161 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.649 |
|
|
\[
{}y^{\prime \prime }+\cos \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.837 |
|
|
\[
{}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.137 |
|
|
\[
{}x \left (x +3\right )^{2} y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.676 |
|
|
\[
{}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.963 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.754 |
|
|
\[
{}\left (x^{3}+4 x \right ) y^{\prime \prime }-2 y^{\prime } x +6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.659 |
|
|
\[
{}x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.933 |
|
|
\[
{}\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.922 |
|
|
\[
{}x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.464 |
|
|
\[
{}x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (5+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.168 |
|
|
\[
{}\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.546 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (x +1\right ) y^{\prime }+\left (x^{2}-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.901 |
|
|
\[
{}x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.490 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.202 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.915 |
|
|
\[
{}2 x y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.148 |
|
|
\[
{}2 x y^{\prime \prime }+5 y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.907 |
|
|
\[
{}4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.108 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.964 |
|
|
\[
{}3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.043 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.135 |
|
|
\[
{}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
1.132 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {4}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.034 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.212 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (2 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.203 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.955 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.991 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.356 |
|
|
\[
{}y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.262 |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.879 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.869 |
|
|
\[
{}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.178 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.076 |
|
|
\[
{}y^{\prime \prime }+\frac {2 y^{\prime }}{t}+\lambda y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.016 |
|
|
\[
{}x^{3} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
0.120 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
0.185 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.997 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
0.897 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.335 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+16 y^{\prime } x +\left (16 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.944 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.884 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+\left (x -\frac {4}{x}\right ) y = 0
\] |
[_Bessel] |
✓ |
1.095 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (9 x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.114 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (36 x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.936 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (25 x^{2}-\frac {4}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.988 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-64\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.134 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.875 |
|
|
\[
{}x y^{\prime \prime }+3 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.945 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.905 |
|
|
\[
{}x y^{\prime \prime }-5 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
1.009 |
|