|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}4 y^{\prime \prime }+\frac {\left (4 x -3\right ) y}{\left (x -1\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.841 |
|
|
\[
{}\left (x -3\right )^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.888 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (-x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.857 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.907 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
0.648 |
|
|
\[
{}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+\left (4 x^{2}+5 x \right ) y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.036 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.825 |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } x +\left (4 x^{3}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.342 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x +\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.824 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.184 |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.099 |
|
|
\[
{}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (x +2\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.011 |
|
|
\[
{}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.179 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +3 y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.920 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.836 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0
\] |
[_Lienard] |
✓ |
0.602 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 y x = 0
\] |
[_Laguerre] |
✓ |
1.252 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (4 x -4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.227 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=1-2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.540 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=6 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.333 |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }+2 x=15 y \\ t y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.058 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=5 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.522 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=8 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.410 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.499 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=5 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.510 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.285 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.327 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=8 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.343 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-13 y \\ y^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.491 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.388 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+2 y-17 \\ y^{\prime }=4 x+y-13 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.579 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+2 y+7 \,{\mathrm e}^{2 t} \\ y^{\prime }=4 x+y-7 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.553 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+3 y-6 \,{\mathrm e}^{3 t} \\ y^{\prime }=x+6 y+2 \,{\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.556 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=4 x+24 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.574 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-13 y \\ y^{\prime }=x+19 \cos \left (4 t \right )-13 \sin \left (4 t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.403 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+3 y+5 \operatorname {Heaviside}\left (t -2\right ) \\ y^{\prime }=x+6 y+17 \operatorname {Heaviside}\left (t -2\right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.643 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=8 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.316 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=3 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.521 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y+4 \\ y^{\prime }=3 x-7 y+5 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.828 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=6 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.326 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x y-6 y \\ y^{\prime }=x-y-5 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.046 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.302 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = x^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.139 |
|
|
\[
{}y y^{\prime }+y^{4} = \sin \left (x \right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.671 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }+5 y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.178 |
|
|
\[
{}{y^{\prime }}^{2}+y = 0
\] |
[_quadrature] |
✓ |
0.483 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.273 |
|
|
\[
{}x {y^{\prime \prime }}^{2}+2 y = 2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.099 |
|
|
\[
{}x^{\prime \prime }+2 \sin \left (x\right ) = \sin \left (2 t \right )
\] |
[NONE] |
✗ |
0.353 |
|
|
\[
{}2 x -1-y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.240 |
|
|
\[
{}2 x -y-y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.219 |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
0.499 |
|
|
\[
{}y^{\prime }+y x = 0
\] |
[_separable] |
✓ |
1.155 |
|
|
\[
{}y^{\prime }+y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.059 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.725 |
|
|
\[
{}y^{\prime \prime }+9 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.244 |
|
|
\[
{}x^{\prime \prime }+2 x^{\prime }-10 x = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.909 |
|
|
\[
{}x^{\prime \prime }+x = t \cos \left (t \right )-\cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.638 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+40 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.401 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.056 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.056 |
|
|
\[
{}x^{2} y^{\prime \prime }-12 y^{\prime } x +42 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.989 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.881 |
|
|
\[
{}y^{\prime } = -\frac {x}{y}
\] |
[_separable] |
✓ |
2.580 |
|
|
\[
{}3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.735 |
|
|
\[
{}y^{\prime } = -\frac {2 y}{x}-3
\] |
[_linear] |
✓ |
1.658 |
|
|
\[
{}y \cos \left (t \right )+\left (2 y+\sin \left (t \right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.077 |
|
|
\[
{}\frac {y}{x}+\cos \left (y\right )+\left (\ln \left (x \right )-x \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
6.383 |
|
|
\[
{}y^{\prime } = \left (x^{2}-1\right ) \left (x^{3}-3 x \right )^{3}
\] |
[_quadrature] |
✓ |
0.295 |
|
|
\[
{}y^{\prime } = x \sin \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
0.290 |
|
|
\[
{}y^{\prime } = \frac {x}{\sqrt {x^{2}-16}}
\] |
[_quadrature] |
✓ |
0.262 |
|
|
\[
{}y^{\prime } = \frac {1}{x \ln \left (x \right )}
\] |
[_quadrature] |
✓ |
0.246 |
|
|
\[
{}y^{\prime } = x \ln \left (x \right )
\] |
[_quadrature] |
✓ |
0.260 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-x}
\] |
[_quadrature] |
✓ |
0.269 |
|
|
\[
{}y^{\prime } = \frac {-2 x -10}{\left (x +2\right ) \left (x -4\right )}
\] |
[_quadrature] |
✓ |
0.293 |
|
|
\[
{}y^{\prime } = \frac {-x^{2}+x}{\left (x +1\right ) \left (x^{2}+1\right )}
\] |
[_quadrature] |
✓ |
0.342 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {x^{2}-16}}{x}
\] |
[_quadrature] |
✓ |
0.348 |
|
|
\[
{}y^{\prime } = \left (-x^{2}+4\right )^{{3}/{2}}
\] |
[_quadrature] |
✓ |
0.314 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}-16}
\] |
[_quadrature] |
✓ |
0.368 |
|
|
\[
{}y^{\prime } = \cos \left (x \right ) \cot \left (x \right )
\] |
[_quadrature] |
✓ |
0.355 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )^{3} \tan \left (x \right )
\] |
[_quadrature] |
✓ |
0.389 |
|
|
\[
{}y^{\prime }+2 y = 0
\] |
[_quadrature] |
✓ |
0.779 |
|
|
\[
{}y^{\prime }+y = \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.281 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.961 |
|
|
\[
{}y^{\prime \prime }+9 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.934 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.119 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.117 |
|
|
\[
{}t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.729 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.477 |
|
|
\[
{}y^{\prime } = 4 x^{3}-x +2
\] |
[_quadrature] |
✓ |
0.355 |
|
|
\[
{}y^{\prime } = \sin \left (2 t \right )-\cos \left (2 t \right )
\] |
[_quadrature] |
✓ |
0.538 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (\frac {1}{x}\right )}{x^{2}}
\] |
[_quadrature] |
✓ |
0.589 |
|
|
\[
{}y^{\prime } = \frac {\ln \left (x \right )}{x}
\] |
[_quadrature] |
✓ |
0.402 |
|
|
\[
{}y^{\prime } = \frac {\left (x -4\right ) y^{3}}{x^{3} \left (y-2\right )}
\] |
[_separable] |
✓ |
2.324 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 y x}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.971 |
|
|
\[
{}y^{\prime } x +y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.060 |
|
|
\[
{}16 y^{\prime \prime }+24 y^{\prime }+153 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.458 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.561 |
|
|
\[
{}4 x \left (x^{2}+y^{2}\right )-5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime } = 0
\] |
[_rational] |
✗ |
30.907 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )^{4}
\] |
[_quadrature] |
✓ |
0.605 |
|