|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime \prime \prime } = \frac {1}{x^{3}}
\] |
[[_high_order, _quadrature]] |
✓ |
0.179 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime } = x +1
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.117 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime } = x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.112 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = {\mathrm e}^{2 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.123 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 12 \,{\mathrm e}^{-x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.130 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.585 |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
0.583 |
|
|
\[
{}y^{\prime }+y = 1
\] |
[_quadrature] |
✓ |
0.355 |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
0.503 |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✗ |
0.085 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.318 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.616 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.558 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.102 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.484 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.519 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.489 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +n^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.645 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 n y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.573 |
|
|
\[
{}x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.125 |
|
|
\[
{}x^{2} \left (x^{2}-1\right )^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.870 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✗ |
0.167 |
|
|
\[
{}\left (3 x +1\right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.283 |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.654 |
|
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.129 |
|
|
\[
{}x^{2} y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.149 |
|
|
\[
{}x^{3} y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.743 |
|
|
\[
{}x^{4} y^{\prime \prime }+\sin \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.129 |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (\cos \left (2 x \right )-1\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.900 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.880 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.797 |
|
|
\[
{}2 x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.777 |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.812 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.850 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y = 0
\] |
[_Lienard] |
✓ |
0.632 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
0.118 |
|
|
\[
{}y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.123 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.780 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.830 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.706 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.911 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.697 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.110 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.793 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
0.855 |
|
|
\[
{}\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.728 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.921 |
|
|
\[
{}\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.895 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (1-3 x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.670 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.964 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✗ |
0.190 |
|
|
\[
{}y^{\prime }+y = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.390 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.216 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.276 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 3 x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.263 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.355 |
|
|
\[
{}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.193 |
|
|
\[
{}x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (4 x +9\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.214 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y = 3 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.324 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
1.782 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = f \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.615 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.359 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.281 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.265 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.604 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.516 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.414 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+t -1 \\ y^{\prime }=3 x+2 y-5 t -2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.501 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.352 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.310 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.402 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=5 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.516 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.389 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.411 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.362 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.379 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+6 y \\ y^{\prime }=2 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.423 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=4 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.500 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-5 t +2 \\ y^{\prime }=4 x-2 y-8 t -8 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.513 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.350 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=4 x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.501 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.400 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+2 y \\ y^{\prime }=-17 x-5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.492 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.383 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.399 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=5 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.579 |
|
|
\[
{}x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.910 |
|
|
\[
{}x^{\prime } = 3 t^{2}+4 t
\] |
[_quadrature] |
✓ |
0.642 |
|
|
\[
{}x^{\prime } = b \,{\mathrm e}^{t}
\] |
[_quadrature] |
✓ |
0.268 |
|
|
\[
{}x^{\prime } = \frac {1}{t^{2}+1}
\] |
[_quadrature] |
✓ |
0.702 |
|
|
\[
{}x^{\prime } = \frac {1}{\sqrt {t^{2}+1}}
\] |
[_quadrature] |
✓ |
0.767 |
|
|
\[
{}x^{\prime } = \cos \left (t \right )
\] |
[_quadrature] |
✓ |
0.751 |
|
|
\[
{}x^{\prime } = \frac {\cos \left (t \right )}{\sin \left (t \right )}
\] |
[_quadrature] |
✓ |
1.062 |
|
|
\[
{}x^{\prime } = x^{2}-3 x+2
\] |
[_quadrature] |
✓ |
2.151 |
|
|
\[
{}x^{\prime } = b \,{\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
0.706 |
|
|
\[
{}x^{\prime } = \left (x-1\right )^{2}
\] |
[_quadrature] |
✓ |
1.308 |
|
|
\[
{}x^{\prime } = \sqrt {x^{2}-1}
\] |
[_quadrature] |
✓ |
4.562 |
|
|
\[
{}x^{\prime } = 2 \sqrt {x}
\] |
[_quadrature] |
✓ |
1.126 |
|
|
\[
{}x^{\prime } = \tan \left (x\right )
\] |
[_quadrature] |
✓ |
2.046 |
|
|
\[
{}3 t^{2} x-t x+\left (3 t^{3} x^{2}+t^{3} x^{4}\right ) x^{\prime } = 0
\] |
[_separable] |
✓ |
2.211 |
|