|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=\frac {3 x}{4}+\frac {5 y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.444 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {3 x}{4}-\frac {7 y}{4} \\ y^{\prime }=\frac {x}{4}+\frac {5 y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.473 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{4}-\frac {3 y}{4} \\ y^{\prime }=\frac {x}{2}+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.475 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.457 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-5 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.457 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+6 y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.446 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.579 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.565 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.566 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-5 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.569 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.563 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-4 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.519 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.519 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-\frac {5 y}{2} \\ y^{\prime }=\frac {9 x}{5}-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.580 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=5 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.551 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=-5 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.546 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-4 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.587 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.557 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.597 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+2 y \\ y^{\prime }=-x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.602 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {3 x}{4}-2 y \\ y^{\prime }=x-\frac {5 y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.548 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {4 x}{5}+2 y \\ y^{\prime }=-x+\frac {6 y}{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.539 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x+y \\ y^{\prime }=-x+a y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.376 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 y \\ y^{\prime }=x+a y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.657 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=a x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.496 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=a x+\frac {5 y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.499 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+a y \\ y^{\prime }=-x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.440 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+a y \\ y^{\prime }=-6 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.511 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x+10 y \\ y^{\prime }=-x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.687 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+a y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.510 |
|
|
\[
{}\left [\begin {array}{c} i^{\prime }=\frac {i}{2}-\frac {v}{8} \\ v^{\prime }=2 i-\frac {v}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.407 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.449 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=-\frac {3 x}{4}-\frac {y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.456 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {3 x}{2}+y \\ y^{\prime }=-\frac {x}{4}-\frac {y}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.464 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+\frac {5 y}{2} \\ y^{\prime }=-\frac {5 x}{2}+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.448 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-\frac {y}{2} \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.461 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+\frac {y}{2} \\ y^{\prime }=-\frac {x}{2}+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.431 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.564 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {5 x}{2}+\frac {3 y}{2} \\ y^{\prime }=-\frac {3 x}{2}+\frac {y}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.582 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+\frac {3 y}{2} \\ y^{\prime }=-\frac {3 x}{2}-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.582 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=-\frac {3 x}{4}-\frac {y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.586 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+\frac {5 y}{2} \\ y^{\prime }=-\frac {5 x}{2}+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.570 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+\frac {y}{2} \\ y^{\prime }=-\frac {x}{2}+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.564 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.537 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.533 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.532 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=8 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.577 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=8 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.574 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-8 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.575 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.583 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.554 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-4 y \\ y^{\prime }=2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.519 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+y+x^{2} \\ y^{\prime }=y-2 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.030 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \,x^{2}-3 x^{2}-4 y \\ y^{\prime }=-2 x \,y^{2}+6 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.033 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-x^{2} \\ y^{\prime }=2 x y-3 y+2 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.031 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x y \\ y^{\prime }=y+2 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.033 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2-y \\ y^{\prime }=y-x^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.031 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x^{2}-x y \\ y^{\prime }=\frac {y}{2}-\frac {y^{2}}{4}-\frac {3 x y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.036 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\left (x-y\right ) \left (1-x-y\right ) \\ y^{\prime }=x \left (2+y\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.034 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \left (2-x-y\right ) \\ y^{\prime }=-x-y-2 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.033 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\left (x+2\right ) \left (y-x\right ) \\ y^{\prime }=y-x^{2}-y^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.033 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 x y \\ y^{\prime }=y-x^{2}-y^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.030 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=x-\frac {x^{3}}{5}-\frac {y}{5} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.031 |
|
|
\[
{}x^{\prime } = \frac {x \sqrt {6 x-9}}{3}
\] |
[_quadrature] |
✓ |
10.248 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \left (1-x-y\right ) \\ y^{\prime }=y \left (\frac {3}{4}-y-\frac {x}{2}\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.036 |
|
|
\[
{}y^{\prime \prime }+t y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.467 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y+y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.970 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\alpha \left (1+\alpha \right ) y = 0
\] |
[_Gegenbauer] |
✗ |
0.950 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-\nu ^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
0.865 |
|
|
\[
{}y^{\prime \prime }+\mu \left (1-y^{2}\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x], _Van_der_Pol] |
✗ |
2.223 |
|
|
\[
{}y^{\prime \prime }-t y = \frac {1}{\pi }
\] |
unknown |
✓ |
3.202 |
|
|
\[
{}a \,x^{2} y^{\prime \prime }+b x y^{\prime }+c y = d
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.440 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.767 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.917 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.385 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.178 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.216 |
|
|
\[
{}t y^{\prime \prime }+3 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.809 |
|
|
\[
{}\left (t -1\right ) y^{\prime \prime }-3 t y^{\prime }+4 y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
1.082 |
|
|
\[
{}t \left (-4+t \right ) y^{\prime \prime }+3 t y^{\prime }+4 y = 2
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
21.906 |
|
|
\[
{}y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+3 \ln \left (t \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.430 |
|
|
\[
{}\left (x +3\right ) y^{\prime \prime }+x y^{\prime }+y \ln \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.664 |
|
|
\[
{}\left (-2+x \right ) y^{\prime \prime }+y^{\prime }+\left (-2+x \right ) \tan \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.815 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\frac {\alpha \left (1+\alpha \right ) \mu ^{2} y}{-x^{2}+1} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
3.449 |
|
|
\[
{}y^{\prime \prime }-\frac {t}{y} = \frac {1}{\pi }
\] |
[NONE] |
✗ |
0.134 |
|
|
\[
{}t^{2} y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.694 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.134 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.244 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.951 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.993 |
|
|
\[
{}\left (1-x \cot \left (x \right )\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
7.372 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.863 |
|
|
\[
{}a y^{\prime \prime }+b y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.109 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.083 |
|
|
\[
{}t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.079 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.081 |
|
|
\[
{}t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.095 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.155 |
|
|
\[
{}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.102 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.103 |
|