|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y = \left (x +2\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.590 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.580 |
|
|
\[
{}x \left (-2+x \right ) y^{\prime \prime }-\left (x^{2}-2\right ) y^{\prime }+2 \left (x -1\right ) y = 3 x^{2} \left (-2+x \right )^{2} {\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.757 |
|
|
\[
{}\left (2 x +1\right ) \left (x +1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = \left (2 x +1\right )^{2}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.826 |
|
|
\[
{}\sin \left (x \right )^{2} y^{\prime \prime }-2 \sin \left (x \right ) \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y = \sin \left (x \right )^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.272 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = x^{2} {\mathrm e}^{x}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.137 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.346 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.966 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.197 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.164 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.440 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.605 |
|
|
\[
{}3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.201 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.411 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.185 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+10 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.034 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.124 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.128 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 x y^{\prime }+18 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.125 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 4 x -6
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.665 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.503 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 4 \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.258 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 2 x \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
5.255 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+4 y = 4 \sin \left (\ln \left (x \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.182 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = x^{3}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.255 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x y^{\prime }-10 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.717 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.165 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.942 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y = 4 x -8
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.385 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = -6 x^{3}+4 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.406 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 10 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.914 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 2 x^{3}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.951 |
|
|
\[
{}x^{2} y^{\prime \prime }-6 y = \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.359 |
|
|
\[
{}\left (x +2\right )^{2} y^{\prime \prime }-\left (x +2\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.054 |
|
|
\[
{}\left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.214 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.508 |
|
|
\[
{}y^{\prime \prime }+8 x y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.555 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.573 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+\left (x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.571 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+\left (2+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.599 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }+\left (3 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.609 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.621 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-\left (3 x -2\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.635 |
|
|
\[
{}\left (x^{3}-1\right ) y^{\prime \prime }+x^{2} y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.615 |
|
|
\[
{}\left (x +3\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.633 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.503 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.544 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.631 |
|
|
\[
{}\left (2 x^{2}-3\right ) y^{\prime \prime }-2 x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.608 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.644 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.675 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.634 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.742 |
|
|
\[
{}\left (x^{2}-3 x \right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.921 |
|
|
\[
{}\left (x^{3}+x^{2}\right ) y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.099 |
|
|
\[
{}\left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.174 |
|
|
\[
{}\left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (-2+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.140 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.792 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.800 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+\frac {8}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.826 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (2 x^{2}+\frac {5}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.817 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.816 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.828 |
|
|
\[
{}3 x y^{\prime \prime }-\left (-2+x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.845 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.765 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.836 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{4}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.803 |
|
|
\[
{}x y^{\prime \prime }-\left (x^{2}+2\right ) y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.785 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.965 |
|
|
\[
{}\left (2 x^{2}-x \right ) y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+\left (-2 x^{2}+3 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.913 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\frac {3 y}{4} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.779 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.252 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.280 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+8 \left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.269 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.347 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.746 |
|
|
\[
{}2 x y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.227 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.759 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}-3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.203 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-2 x-4 y={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-y={\mathrm e}^{4 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.232 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=-2 t \\ x^{\prime }+y^{\prime }-3 x-y=t^{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.190 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-3 y={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }+x={\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.169 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-2 y=2 \,{\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-3 x-4 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.108 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y={\mathrm e}^{-t} \\ x^{\prime }+2 x+y^{\prime }+y={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.685 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-3 x-y=t \\ x^{\prime }+y^{\prime }-4 x-y={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.496 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-6 y={\mathrm e}^{3 t} \\ x^{\prime }+2 y^{\prime }-2 x-6 y=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.655 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-3 y=3 t \\ x^{\prime }+2 y^{\prime }-2 x-3 y=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.653 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }+2 y=\sin \left (t \right ) \\ x^{\prime }+y^{\prime }-x-y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.220 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-y^{\prime }-2 x+4 y=t \\ x^{\prime }+y^{\prime }-x-y=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.490 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }+x+5 y=4 t \\ x^{\prime }+y^{\prime }+2 x+2 y=2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.483 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x+5 y=t^{2} \\ x^{\prime }+2 y^{\prime }-2 x+4 y=2 t +1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.420 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }+x+y=t^{2}+4 t \\ x^{\prime }+y^{\prime }+2 x+2 y=2 t^{2}-2 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.484 |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }+2 y^{\prime }-x+y=t -1 \\ x^{\prime }+y^{\prime }-x=t +2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.628 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+4 y^{\prime }+x-y=3 \,{\mathrm e}^{t} \\ x^{\prime }+y^{\prime }+2 x+2 y={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.500 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y=-2 t \\ x^{\prime }+y^{\prime }+x-y=t^{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.494 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y=1 \\ x^{\prime }+y^{\prime }+2 x-y=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.482 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.460 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+3 y \\ y^{\prime }=4 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.462 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+2 y+5 t \\ y^{\prime }=3 x+4 y+17 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.513 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.316 |
|