|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}-y^{2} y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.388 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }=2 x_{1}-9 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.411 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+3 x_{2} \\ x_{2}^{\prime }=5 x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.314 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+3 x_{2} \\ x_{2}^{\prime }=-3 x_{1}+5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.391 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}+2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.421 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.315 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t} \\ x_{2}^{\prime }=x_{1}-2 x_{2}+3 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.480 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=16 x_{1}-5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.457 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=3 x_{1}-4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.424 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }=2 x_{1}-9 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.476 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+3 x_{2} \\ x_{2}^{\prime }=-3 x_{1}+5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.446 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }=2 x_{1}-9 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.400 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.406 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-8 \\ x_{2}^{\prime }=x_{1}+x_{2}+3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.477 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-8 \\ x_{2}^{\prime }=x_{1}+x_{2}+3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.557 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{3 x}+\sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.316 |
|
|
\[
{}y^{\prime \prime } = x +2
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.095 |
|
|
\[
{}y^{\prime \prime \prime } = x^{2}
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.096 |
|
|
\[
{}y^{\prime }+\cos \left (x \right ) y = 0
\] |
[_separable] |
✓ |
1.212 |
|
|
\[
{}y^{\prime }+\cos \left (x \right ) y = \sin \left (x \right ) \cos \left (x \right )
\] |
[_linear] |
✓ |
1.506 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.769 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.721 |
|
|
\[
{}y^{\prime \prime }+k^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.526 |
|
|
\[
{}y^{\prime }+5 y = 2
\] |
[_quadrature] |
✓ |
0.559 |
|
|
\[
{}y^{\prime \prime } = 3 x +1
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.095 |
|
|
\[
{}y^{\prime } = k y
\] |
[_quadrature] |
✓ |
0.378 |
|
|
\[
{}y^{\prime }-2 y = 1
\] |
[_quadrature] |
✓ |
0.371 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.891 |
|
|
\[
{}y^{\prime }-2 y = x^{2}+x
\] |
[[_linear, ‘class A‘]] |
✓ |
0.921 |
|
|
\[
{}3 y^{\prime }+y = 2 \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.070 |
|
|
\[
{}y^{\prime }+3 y = {\mathrm e}^{i x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.781 |
|
|
\[
{}y^{\prime }+i y = x
\] |
[[_linear, ‘class A‘]] |
✓ |
0.864 |
|
|
\[
{}L y^{\prime }+R y = E
\] |
[_quadrature] |
✓ |
0.373 |
|
|
\[
{}L y^{\prime }+R y = E \sin \left (\omega x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.474 |
|
|
\[
{}L y^{\prime }+R y = E \,{\mathrm e}^{i \omega x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.108 |
|
|
\[
{}y^{\prime }+a y = b \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.121 |
|
|
\[
{}y^{\prime }+2 y x = x
\] |
[_separable] |
✓ |
0.984 |
|
|
\[
{}y^{\prime } x +y = 3 x^{3}-1
\] |
[_linear] |
✓ |
0.911 |
|
|
\[
{}y^{\prime }+y \,{\mathrm e}^{x} = 3 \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
1.146 |
|
|
\[
{}y^{\prime }-\tan \left (x \right ) y = {\mathrm e}^{\sin \left (x \right )}
\] |
[_linear] |
✓ |
1.490 |
|
|
\[
{}y^{\prime }+2 y x = x \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
2.068 |
|
|
\[
{}y^{\prime }+\cos \left (x \right ) y = {\mathrm e}^{-\sin \left (x \right )}
\] |
[_linear] |
✓ |
1.592 |
|
|
\[
{}x^{2} y^{\prime }+2 y x = 1
\] |
[_linear] |
✓ |
1.069 |
|
|
\[
{}y^{\prime }+2 y = b \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.094 |
|
|
\[
{}y^{\prime } = 1+y
\] |
[_quadrature] |
✓ |
0.394 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.566 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.552 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.937 |
|
|
\[
{}3 y^{\prime \prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.727 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.720 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.202 |
|
|
\[
{}y^{\prime \prime }+2 i y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.905 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.141 |
|
|
\[
{}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.721 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.970 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.943 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.789 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.520 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.490 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.549 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.972 |
|
|
\[
{}y^{\prime \prime }+\left (1+4 i\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.588 |
|
|
\[
{}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.816 |
|
|
\[
{}y^{\prime \prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.414 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.297 |
|
|
\[
{}y^{\prime \prime }+9 y = \sin \left (3 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.760 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.776 |
|
|
\[
{}y^{\prime \prime }+2 i y^{\prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.643 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x}+2 x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.141 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.341 |
|
|
\[
{}y^{\prime \prime }+y = 2 \sin \left (x \right ) \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.081 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.217 |
|
|
\[
{}4 y^{\prime \prime }-y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.896 |
|
|
\[
{}6 y^{\prime \prime }+5 y^{\prime }-6 y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.973 |
|
|
\[
{}y^{\prime \prime }+\omega ^{2} y = A \cos \left (\omega x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.556 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }+6 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.062 |
|
|
\[
{}y^{\prime \prime \prime }-i y^{\prime \prime }+4 y^{\prime }-4 i y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.081 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.068 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime }-2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.063 |
|
|
\[
{}y^{\prime \prime \prime }-3 i y^{\prime \prime }-3 y^{\prime }+i y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.114 |
|
|
\[
{}y^{\left (5\right )}-y^{\prime \prime \prime \prime }-y^{\prime }+y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.659 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.733 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.067 |
|
|
\[
{}y^{\left (5\right )}+2 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.145 |
|
|
\[
{}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.063 |
|
|
\[
{}y^{\prime \prime \prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.134 |
|
|
\[
{}y^{\prime \prime \prime }-i y^{\prime \prime }+y^{\prime }-i y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.081 |
|
|
\[
{}y^{\prime \prime }-2 i y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.597 |
|
|
\[
{}y^{\prime \prime \prime \prime }-k^{4} y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.157 |
|
|
\[
{}y^{\prime \prime \prime }-y = x
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.108 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = {\mathrm e}^{i x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.470 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.135 |
|
|
\[
{}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.121 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = \cos \left (x \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.490 |
|
|
\[
{}y^{\prime \prime }-2 i y^{\prime }-y = {\mathrm e}^{i x}-2 \,{\mathrm e}^{-i x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.003 |
|