|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.408 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=8 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.450 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=8 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.454 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-8 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.499 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.434 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.435 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-4 y \\ y^{\prime }=2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.373 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+y+x^{2} \\ y^{\prime }=y-2 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.049 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \,x^{2}-3 x^{2}-4 y \\ y^{\prime }=-2 x \,y^{2}+6 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.054 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-x^{2} \\ y^{\prime }=2 x y-3 y+2 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.051 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x y \\ y^{\prime }=y+2 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.049 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2-y \\ y^{\prime }=y-x^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.051 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x^{2}-x y \\ y^{\prime }=\frac {y}{2}-\frac {y^{2}}{4}-\frac {3 x y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.051 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\left (x-y\right ) \left (1-x-y\right ) \\ y^{\prime }=x \left (2+y\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.052 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \left (2-x-y\right ) \\ y^{\prime }=-x-y-2 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.053 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\left (x+2\right ) \left (y-x\right ) \\ y^{\prime }=y-x^{2}-y^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.052 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 x y \\ y^{\prime }=y-x^{2}-y^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.051 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=x-\frac {x^{3}}{5}-\frac {y}{5} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.050 |
|
|
\[
{}x^{\prime } = \frac {x \sqrt {6 x-9}}{3}
\] |
[_quadrature] |
✓ |
185.478 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \left (1-x-y\right ) \\ y^{\prime }=y \left (\frac {3}{4}-y-\frac {x}{2}\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.060 |
|
|
\[
{}y^{\prime \prime }+t y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.688 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y+y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.490 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\alpha \left (1+\alpha \right ) y = 0
\] |
[_Gegenbauer] |
✗ |
0.939 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-\nu ^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
2.092 |
|
|
\[
{}y^{\prime \prime }+\mu \left (1-y^{2}\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x], _Van_der_Pol] |
✗ |
0.558 |
|
|
\[
{}y^{\prime \prime }-t y = \frac {1}{\pi }
\] |
unknown |
✓ |
3.339 |
|
|
\[
{}a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = d
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.599 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.017 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.144 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.446 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.116 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.019 |
|
|
\[
{}t y^{\prime \prime }+3 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.128 |
|
|
\[
{}\left (t -1\right ) y^{\prime \prime }-3 t y^{\prime }+4 y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
1.054 |
|
|
\[
{}t \left (-4+t \right ) y^{\prime \prime }+3 t y^{\prime }+4 y = 2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
8.010 |
|
|
\[
{}y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 \ln \left (t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.650 |
|
|
\[
{}\left (x +3\right ) y^{\prime \prime }+x y^{\prime }+y \ln \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.396 |
|
|
\[
{}\left (-2+x \right ) y^{\prime \prime }+y^{\prime }+\left (-2+x \right ) \tan \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.687 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\frac {\alpha \left (1+\alpha \right ) \mu ^{2} y}{-x^{2}+1} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.886 |
|
|
\[
{}y^{\prime \prime }-\frac {t}{y} = \frac {1}{\pi }
\] |
[NONE] |
✗ |
0.094 |
|
|
\[
{}t^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.913 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.404 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.992 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.829 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.238 |
|
|
\[
{}\left (1-x \cot \left (x \right )\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.622 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.838 |
|
|
\[
{}a y^{\prime \prime }+b y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.340 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.314 |
|
|
\[
{}t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.312 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.316 |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.336 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.401 |
|
|
\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.340 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.333 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.399 |
|
|
\[
{}x y^{\prime \prime }-\left (x +n \right ) y^{\prime }+n y = 0
\] |
[_Laguerre] |
✓ |
0.398 |
|
|
\[
{}y^{\prime \prime }+a \left (x y^{\prime }+y\right ) = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.355 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.830 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.815 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.856 |
|
|
\[
{}9 y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.867 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.272 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.016 |
|
|
\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.862 |
|
|
\[
{}2 y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.810 |
|
|
\[
{}6 y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.845 |
|
|
\[
{}9 y^{\prime \prime }+12 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.867 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.859 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.276 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.388 |
|
|
\[
{}4 y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.174 |
|
|
\[
{}25 y^{\prime \prime }-20 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.850 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.201 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.768 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.537 |
|
|
\[
{}y^{\prime \prime }-9 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.102 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.067 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.858 |
|
|
\[
{}9 y^{\prime \prime }-24 y^{\prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.850 |
|
|
\[
{}4 y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.983 |
|
|
\[
{}4 y^{\prime \prime }+9 y^{\prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.865 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.314 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.607 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.397 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.679 |
|
|
\[
{}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.243 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.070 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.059 |
|
|
\[
{}6 y^{\prime \prime }-5 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.121 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.173 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.991 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.007 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.943 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.207 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.599 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.191 |
|
|
\[
{}2 y^{\prime \prime }+y^{\prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.552 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.439 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.220 |
|