|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.067 |
|
|
\[
{}x^{2} y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.343 |
|
|
\[
{}x^{3} y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.477 |
|
|
\[
{}x^{4} y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.106 |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (\cos \left (2 x \right )-1\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.778 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.805 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.056 |
|
|
\[
{}2 x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.816 |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.065 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.799 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0
\] |
[_Lienard] |
✓ |
0.629 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
0.105 |
|
|
\[
{}y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.324 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.742 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.809 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.763 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.867 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.678 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.535 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.040 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
0.913 |
|
|
\[
{}\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.951 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.964 |
|
|
\[
{}\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.939 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (1-3 x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.675 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
1.229 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✗ |
0.136 |
|
|
\[
{}y^{\prime }+y = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.259 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.234 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.554 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 3 x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.290 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.395 |
|
|
\[
{}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.260 |
|
|
\[
{}x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (4 x +9\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.308 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y = 3 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.454 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
2.508 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = f \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.597 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.333 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.260 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.327 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.552 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.638 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.538 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+t -1 \\ y^{\prime }=3 x+2 y-5 t -2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.734 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.440 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.431 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.513 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=5 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.665 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.525 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.524 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.467 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.276 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+6 y \\ y^{\prime }=2 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.336 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=4 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.594 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-5 t +2 \\ y^{\prime }=4 x-2 y-8 t -8 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.793 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.479 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=4 x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.590 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.514 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+2 y \\ y^{\prime }=-17 x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.589 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.485 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.530 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=5 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.619 |
|
|
\[
{}x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
2.864 |
|
|
\[
{}x^{\prime } = 3 t^{2}+4 t
\] |
[_quadrature] |
✓ |
0.604 |
|
|
\[
{}x^{\prime } = b \,{\mathrm e}^{t}
\] |
[_quadrature] |
✓ |
0.288 |
|
|
\[
{}x^{\prime } = \frac {1}{t^{2}+1}
\] |
[_quadrature] |
✓ |
0.587 |
|
|
\[
{}x^{\prime } = \frac {1}{\sqrt {t^{2}+1}}
\] |
[_quadrature] |
✓ |
0.337 |
|
|
\[
{}x^{\prime } = \cos \left (t \right )
\] |
[_quadrature] |
✓ |
0.624 |
|
|
\[
{}x^{\prime } = \frac {\cos \left (t \right )}{\sin \left (t \right )}
\] |
[_quadrature] |
✓ |
1.611 |
|
|
\[
{}x^{\prime } = x^{2}-3 x+2
\] |
[_quadrature] |
✓ |
3.632 |
|
|
\[
{}x^{\prime } = b \,{\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
1.309 |
|
|
\[
{}x^{\prime } = \left (x-1\right )^{2}
\] |
[_quadrature] |
✓ |
1.022 |
|
|
\[
{}x^{\prime } = \sqrt {x^{2}-1}
\] |
[_quadrature] |
✓ |
10.636 |
|
|
\[
{}x^{\prime } = 2 \sqrt {x}
\] |
[_quadrature] |
✓ |
1.392 |
|
|
\[
{}x^{\prime } = \tan \left (x\right )
\] |
[_quadrature] |
✓ |
1.497 |
|
|
\[
{}3 t^{2} x-x t +\left (3 t^{3} x^{2}+t^{3} x^{4}\right ) x^{\prime } = 0
\] |
[_separable] |
✓ |
3.056 |
|
|
\[
{}1+2 x+\left (-t^{2}+4\right ) x^{\prime } = 0
\] |
[_separable] |
✓ |
1.865 |
|
|
\[
{}x^{\prime } = \cos \left (\frac {x}{t}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.161 |
|
|
\[
{}\left (t^{2}-x^{2}\right ) x^{\prime } = x t
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.648 |
|
|
\[
{}{\mathrm e}^{3 t} x^{\prime }+3 x \,{\mathrm e}^{3 t} = 2 t
\] |
[[_linear, ‘class A‘]] |
✓ |
2.059 |
|
|
\[
{}2 t +3 x+\left (3 t -x\right ) x^{\prime } = t^{2}
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.880 |
|
|
\[
{}x^{\prime }+2 x = {\mathrm e}^{t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.134 |
|
|
\[
{}x^{\prime }+x \tan \left (t \right ) = 0
\] |
[_separable] |
✓ |
1.074 |
|
|
\[
{}x^{\prime }-x \tan \left (t \right ) = 4 \sin \left (t \right )
\] |
[_linear] |
✓ |
1.561 |
|
|
\[
{}t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x = t^{3}
\] |
[_linear] |
✓ |
1.909 |
|
|
\[
{}x^{\prime }+2 x t +t x^{4} = 0
\] |
[_separable] |
✓ |
2.093 |
|
|
\[
{}x^{\prime } t +x \ln \left (t \right ) = t^{2}
\] |
[_linear] |
✓ |
1.716 |
|
|
\[
{}x^{\prime } t +x g \left (t \right ) = h \left (t \right )
\] |
[_linear] |
✓ |
1.616 |
|
|
\[
{}t^{2} x^{\prime \prime }-6 x^{\prime } t +12 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.117 |
|
|
\[
{}x^{\prime } = -\lambda x
\] |
[_quadrature] |
✓ |
0.807 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.421 |
|
|
\[
{}t^{2} x^{\prime \prime }-2 x^{\prime } t +2 x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.280 |
|
|
\[
{}x^{\prime \prime }-5 x^{\prime }+6 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.515 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.495 |
|
|
\[
{}x^{\prime \prime }-4 x^{\prime }+5 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.888 |
|
|
\[
{}x^{\prime \prime }+3 x^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.013 |
|
|
\[
{}x^{\prime \prime }-3 x^{\prime }+2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.717 |
|
|
\[
{}x^{\prime \prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.932 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.742 |
|
|
\[
{}x^{\prime \prime }-2 x^{\prime }+2 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.891 |
|