|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (x^{3}+x^{2}\right ) y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.983 |
|
|
\[
{}\left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.163 |
|
|
\[
{}\left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.123 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.740 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.747 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+\frac {8}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.768 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (2 x^{2}+\frac {5}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.755 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.741 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.780 |
|
|
\[
{}3 x y^{\prime \prime }-\left (x -2\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.802 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
0.694 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.785 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{4}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.764 |
|
|
\[
{}x y^{\prime \prime }-\left (x^{2}+2\right ) y^{\prime }+y x = 0
\] |
[_Lienard] |
✓ |
0.762 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.883 |
|
|
\[
{}\left (2 x^{2}-x \right ) y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+\left (-2 x^{2}+3 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.863 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\frac {3 y}{4} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.724 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.176 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.174 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +8 \left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.252 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.267 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.704 |
|
|
\[
{}2 x y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.132 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.718 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.122 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-2 x-4 y={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-y={\mathrm e}^{4 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.234 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=-2 t \\ x^{\prime }+y^{\prime }-3 x-y=t^{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.179 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-3 y={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }+x={\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.163 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-2 y=2 \,{\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-3 x-4 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.105 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y={\mathrm e}^{-t} \\ x^{\prime }+2 x+y^{\prime }+y={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.644 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-3 x-y=t \\ x^{\prime }+y^{\prime }-4 x-y={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.464 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-6 y={\mathrm e}^{3 t} \\ x^{\prime }+2 y^{\prime }-2 x-6 y=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.630 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-3 y=3 t \\ x^{\prime }+2 y^{\prime }-2 x-3 y=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.622 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }+2 y=\sin \left (t \right ) \\ x^{\prime }+y^{\prime }-x-y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.211 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-y^{\prime }-2 x+4 y=t \\ x^{\prime }+y^{\prime }-x-y=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.473 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }+x+5 y=4 t \\ x^{\prime }+y^{\prime }+2 x+2 y=2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.445 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x+5 y=t^{2} \\ x^{\prime }+2 y^{\prime }-2 x+4 y=2 t +1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.368 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }+x+y=t^{2}+4 t \\ x^{\prime }+y^{\prime }+2 x+2 y=2 t^{2}-2 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.463 |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }+2 y^{\prime }-x+y=t -1 \\ x^{\prime }+y^{\prime }-x=t +2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.585 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+4 y^{\prime }+x-y=3 \,{\mathrm e}^{t} \\ x^{\prime }+y^{\prime }+2 x+2 y={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.487 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y=-2 t \\ x^{\prime }+y^{\prime }+x-y=t^{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.463 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y=1 \\ x^{\prime }+y^{\prime }+2 x-y=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.454 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.452 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+3 y \\ y^{\prime }=4 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.471 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+2 y+5 t \\ y^{\prime }=3 x+4 y+17 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.486 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.299 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.296 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+7 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.396 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=7 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.489 |
|
|
\(\left [\begin {array}{cc} 1 & 2 \\ 3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.142 |
|
|
\(\left [\begin {array}{cc} 3 & 2 \\ 6 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.137 |
|
|
\(\left [\begin {array}{cc} 3 & 1 \\ 12 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.141 |
|
|
\(\left [\begin {array}{cc} -2 & 7 \\ 3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.138 |
|
|
\(\left [\begin {array}{cc} 3 & 4 \\ 5 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.137 |
|
|
\(\left [\begin {array}{cc} 3 & -5 \\ -4 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.138 |
|
|
\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ 2 & 3 & -4 \\ 4 & 1 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.235 |
|
|
\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & -6 & 6 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.240 |
|
|
\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & 1 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.232 |
|
|
\(\left [\begin {array}{ccc} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.210 |
|
|
\(\left [\begin {array}{ccc} 1 & 3 & -6 \\ 0 & 2 & 2 \\ 0 & -1 & 5 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.213 |
|
|
\(\left [\begin {array}{ccc} -5 & -12 & 6 \\ 1 & 5 & -1 \\ -7 & -10 & 8 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.243 |
|
|
\(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.238 |
|
|
\(\left [\begin {array}{ccc} -2 & 6 & -18 \\ 12 & -23 & 66 \\ 5 & -10 & 29 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.238 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-z \\ y^{\prime }=2 x+3 y-4 z \\ z^{\prime }=4 x+y-4 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.495 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y-z \\ y^{\prime }=x+3 y+z \\ z^{\prime }=-3 x-6 y+6 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.481 |
|
|
\[
{}x^{\prime } = \sin \left (t \right )+\cos \left (t \right )
\] |
[_quadrature] |
✓ |
0.301 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}-1}
\] |
[_quadrature] |
✓ |
0.249 |
|
|
\[
{}u^{\prime } = 4 t \ln \left (t \right )
\] |
[_quadrature] |
✓ |
0.268 |
|
|
\[
{}z^{\prime } = x \,{\mathrm e}^{-2 x}
\] |
[_quadrature] |
✓ |
0.270 |
|
|
\[
{}T^{\prime } = {\mathrm e}^{-t} \sin \left (2 t \right )
\] |
[_quadrature] |
✓ |
0.341 |
|
|
\[
{}x^{\prime } = \sec \left (t \right )^{2}
\] |
[_quadrature] |
✓ |
0.546 |
|
|
\[
{}y^{\prime } = x -\frac {1}{3} x^{3}
\] |
[_quadrature] |
✓ |
0.358 |
|
|
\[
{}x^{\prime } = 2 \sin \left (t \right )^{2}
\] |
[_quadrature] |
✓ |
0.524 |
|
|
\[
{}x V^{\prime } = x^{2}+1
\] |
[_quadrature] |
✓ |
0.425 |
|
|
\[
{}x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = {\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.344 |
|
|
\[
{}x^{\prime } = -x+1
\] |
[_quadrature] |
✓ |
0.339 |
|
|
\[
{}x^{\prime } = x \left (2-x\right )
\] |
[_quadrature] |
✓ |
0.787 |
|
|
\[
{}x^{\prime } = \left (1+x\right ) \left (2-x\right ) \sin \left (x\right )
\] |
[_quadrature] |
✓ |
4.307 |
|
|
\[
{}x^{\prime } = -x \left (-x+1\right ) \left (2-x\right )
\] |
[_quadrature] |
✓ |
1.620 |
|
|
\[
{}x^{\prime } = x^{2}-x^{4}
\] |
[_quadrature] |
✓ |
0.607 |
|
|
\[
{}x^{\prime } = t^{3} \left (-x+1\right )
\] |
[_separable] |
✓ |
1.253 |
|
|
\[
{}y^{\prime } = \left (1+y^{2}\right ) \tan \left (x \right )
\] |
[_separable] |
✓ |
3.076 |
|
|
\[
{}x^{\prime } = t^{2} x
\] |
[_separable] |
✓ |
1.007 |
|
|
\[
{}x^{\prime } = -x^{2}
\] |
[_quadrature] |
✓ |
0.382 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-t^{2}} y^{2}
\] |
[_separable] |
✓ |
1.447 |
|
|
\[
{}x^{\prime }+p x = q
\] |
[_quadrature] |
✓ |
0.334 |
|
|
\[
{}y^{\prime } x = k y
\] |
[_separable] |
✓ |
1.189 |
|
|
\[
{}i^{\prime } = p \left (t \right ) i
\] |
[_separable] |
✓ |
0.993 |
|
|
\[
{}x^{\prime } = \lambda x
\] |
[_quadrature] |
✓ |
0.367 |
|
|
\[
{}m v^{\prime } = -m g +k v^{2}
\] |
[_quadrature] |
✓ |
0.364 |
|
|
\[
{}x^{\prime } = k x-x^{2}
\] |
[_quadrature] |
✓ |
1.146 |
|
|
\[
{}x^{\prime } = -x \left (k^{2}+x^{2}\right )
\] |
[_quadrature] |
✓ |
1.825 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x^{2}
\] |
[_linear] |
✓ |
1.115 |
|
|
\[
{}x^{\prime }+x t = 4 t
\] |
[_separable] |
✓ |
1.478 |
|
|
\[
{}z^{\prime } = z \tan \left (y \right )+\sin \left (y \right )
\] |
[_linear] |
✓ |
1.520 |
|
|
\[
{}y^{\prime }+{\mathrm e}^{-x} y = 1
\] |
[_linear] |
✓ |
1.208 |
|
|
\[
{}x^{\prime }+x \tanh \left (t \right ) = 3
\] |
[_linear] |
✓ |
1.046 |
|
|
\[
{}y^{\prime }+2 y \cot \left (x \right ) = 5
\] |
[_linear] |
✓ |
1.364 |
|
|
\[
{}x^{\prime }+5 x = t
\] |
[[_linear, ‘class A‘]] |
✓ |
0.842 |
|
|
\[
{}x^{\prime }+\left (a +\frac {1}{t}\right ) x = b
\] |
[_linear] |
✓ |
1.047 |
|