|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-4 y = {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.197 |
|
|
\[
{}y^{\prime \prime }-y = x^{2} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.193 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 10 x^{3} {\mathrm e}^{-2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.247 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.166 |
|
|
\[
{}y^{\prime \prime }-y = {\mathrm e}^{-x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.151 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 6 \,{\mathrm e}^{5 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.135 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+y = x^{3}-3 x^{2}+1
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
32.030 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime }+y = 2 x^{3}-3 x^{2}+4 x +5
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.117 |
|
|
\[
{}4 y^{\prime \prime }+y = x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.556 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime } = x^{2}
\] |
[[_high_order, _missing_y]] |
✓ |
0.111 |
|
|
\[
{}y^{\left (6\right )}-y = x^{10}
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.167 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-y = -x^{4}+3 x
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.621 |
|
|
\[
{}y^{\prime \prime }+y = x^{4}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.985 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime } = 12 x -2
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.094 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } = 9 x^{2}-2 x +1
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.103 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = x^{3} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.226 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = {\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.302 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 x^{2} {\mathrm e}^{-2 x}+3 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.358 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = 16 x^{2}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.105 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = -x^{3}+1
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.107 |
|
|
\[
{}y^{\prime \prime \prime }-\frac {y^{\prime }}{4} = x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.090 |
|
|
\[
{}y^{\prime \prime \prime \prime } = \frac {1}{x^{3}}
\] |
[[_high_order, _quadrature]] |
✓ |
0.175 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime } = x +1
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.100 |
|
|
\[
{}y^{\prime \prime \prime }+2 y^{\prime \prime } = x
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.094 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = {\mathrm e}^{2 x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.113 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 12 \,{\mathrm e}^{-x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.120 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.392 |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
0.365 |
|
|
\[
{}y^{\prime }+y = 1
\] |
[_quadrature] |
✓ |
0.343 |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
0.273 |
|
|
\[
{}x^{2} y^{\prime } = y
\] |
[_separable] |
✗ |
0.061 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.293 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.467 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.358 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.059 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.335 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.368 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.236 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+n^{2} y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.476 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+2 n y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.390 |
|
|
\[
{}x^{3} \left (-1+x \right ) y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }+3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.110 |
|
|
\[
{}x^{2} \left (x^{2}-1\right )^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.634 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✗ |
0.145 |
|
|
\[
{}\left (3 x +1\right ) x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.444 |
|
|
\[
{}y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.470 |
|
|
\[
{}x y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.018 |
|
|
\[
{}x^{2} y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.171 |
|
|
\[
{}x^{3} y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.542 |
|
|
\[
{}x^{4} y^{\prime \prime }+y \sin \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.112 |
|
|
\[
{}x^{3} y^{\prime \prime }+\left (\cos \left (2 x \right )-1\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.724 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.723 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.684 |
|
|
\[
{}2 x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.655 |
|
|
\[
{}2 x y^{\prime \prime }+\left (x +1\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.708 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.720 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0
\] |
[_Lienard] |
✓ |
0.434 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
0.102 |
|
|
\[
{}y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.104 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.666 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.717 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.588 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.741 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.504 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.211 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.668 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
0.732 |
|
|
\[
{}\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.596 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.768 |
|
|
\[
{}\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.748 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+\left (1-3 x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.469 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
0.807 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-n^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✗ |
0.180 |
|
|
\[
{}y^{\prime }+y = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.381 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.204 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.340 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } = 3 x^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.321 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.409 |
|
|
\[
{}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.181 |
|
|
\[
{}x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (4 x +9\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.215 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y = 3 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.361 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
1.633 |
|
|
\[
{}y^{\prime \prime }+a^{2} y = f \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.445 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.414 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.332 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.320 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.413 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.559 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.463 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+t -1 \\ y^{\prime }=3 x+2 y-5 t -2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.588 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.405 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.297 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.442 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=5 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.581 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.457 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.461 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.407 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.431 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+6 y \\ y^{\prime }=2 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.485 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=4 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.571 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-5 t +2 \\ y^{\prime }=4 x-2 y-8 t -8 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.540 |
|