|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 y \\ y^{\prime }=3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.851 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.070 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y+3 \,{\mathrm e}^{t} \\ y^{\prime }=5 x-y-t^{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.927 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x t -{\mathrm e}^{t} y+\cos \left (t \right ) \\ y^{\prime }={\mathrm e}^{-t} x+t^{2} y-\sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.053 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+z \\ y^{\prime }=x+z \\ z^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.377 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-3 y \\ y^{\prime }=x+y+2 z \\ z^{\prime }=5 y-7 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
9.258 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y+z+t \\ y^{\prime }=x-3 z+t^{2} \\ z^{\prime }=6 y-7 z+t^{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
103.527 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x t -y+{\mathrm e}^{t} z \\ y^{\prime }=2 x+t^{2} y-z \\ z^{\prime }={\mathrm e}^{-t} x+3 t y+t^{3} z \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.084 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=2 x_{3} \\ x_{3}^{\prime }=3 x_{4} \\ x_{4}^{\prime }=4 x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
3.334 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+x_{3}+1 \\ x_{2}^{\prime }=x_{3}+x_{4}+t \\ x_{3}^{\prime }=x_{1}+x_{4}+t^{2} \\ x_{4}^{\prime }=x_{1}+x_{2}+t^{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
3.444 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+2 x_{2} \\ x_{2}^{\prime }=-3 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.370 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=-3 x_{1}+4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.342 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.338 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2} \\ x_{2}^{\prime }=-2 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.310 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-3 x_{2} \\ x_{2}^{\prime }=6 x_{1}-7 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.359 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=-x_{1}+3 x_{2}-2 x_{3} \\ x_{3}^{\prime }=-x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.119 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.026 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+x_{3} \\ x_{2}^{\prime }=6 x_{1}-x_{2} \\ x_{3}^{\prime }=-x_{1}-2 x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.169 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-8 x_{1}-11 x_{2}-2 x_{3} \\ x_{2}^{\prime }=6 x_{1}+9 x_{2}+2 x_{3} \\ x_{3}^{\prime }=-6 x_{1}-6 x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.520 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2}-2 x_{4} \\ x_{2}^{\prime }=x_{2} \\ x_{3}^{\prime }=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\ x_{4}^{\prime }=-4 x_{2}-x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.180 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.306 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+3 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.934 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+4 x_{2} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.337 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2} \\ x_{2}^{\prime }=6 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.966 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=6 x_{1}-7 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.276 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}+5 x_{2} \\ x_{2}^{\prime }=-6 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.990 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }=6 x_{1}-5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.289 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.023 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.364 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=9 x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.994 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.345 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.033 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-9 x_{2} \\ x_{2}^{\prime }=2 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.357 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.970 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-5 x_{2} \\ x_{2}^{\prime }=4 x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.403 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-50 x_{1}+20 x_{2} \\ x_{2}^{\prime }=100 x_{1}-60 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.971 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+4 x_{3} \\ x_{2}^{\prime }=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }=4 x_{1}+x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.413 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }=2 x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}+7 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.072 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+4 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.013 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }=3 x_{1}+x_{2}+5 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.413 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-6 x_{3} \\ x_{2}^{\prime }=2 x_{1}-x_{2}-2 x_{3} \\ x_{3}^{\prime }=4 x_{1}-2 x_{2}-4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.132 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-5 x_{1}-4 x_{2}-2 x_{3} \\ x_{3}^{\prime }=5 x_{1}+5 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.108 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=-5 x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }=5 x_{1}+5 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.174 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }=-4 x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }=4 x_{1}+4 x_{2}+2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.694 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+5 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-6 x_{1}-6 x_{2}-5 x_{3} \\ x_{3}^{\prime }=6 x_{1}+6 x_{2}+5 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.286 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{3} \\ x_{2}^{\prime }=9 x_{1}-x_{2}+2 x_{3} \\ x_{3}^{\prime }=-9 x_{1}+4 x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.377 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=2 x_{1}+2 x_{2} \\ x_{3}^{\prime }=3 x_{2}+3 x_{3} \\ x_{4}^{\prime }=4 x_{3}+4 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.493 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+9 x_{4} \\ x_{2}^{\prime }=4 x_{1}+2 x_{2}-10 x_{4} \\ x_{3}^{\prime }=-x_{3}+8 x_{4} \\ x_{4}^{\prime }=x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.382 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\ x_{3}^{\prime }=5 x_{3} \\ x_{4}^{\prime }=-21 x_{3}-2 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.450 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\ x_{2}^{\prime }=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\ x_{3}^{\prime }=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\ x_{4}^{\prime }=7 x_{1}+x_{2}+x_{3}+4 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
2.191 |
|
|
\[
{}y^{\prime } = 2 x +1
\] |
[_quadrature] |
✓ |
0.290 |
|
|
\[
{}y^{\prime } = \left (x -2\right )^{2}
\] |
[_quadrature] |
✓ |
0.932 |
|
|
\[
{}y^{\prime } = \sqrt {x}
\] |
[_quadrature] |
✓ |
0.325 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}}
\] |
[_quadrature] |
✓ |
0.900 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {x +2}}
\] |
[_quadrature] |
✓ |
0.324 |
|
|
\[
{}y^{\prime } = x \sqrt {x^{2}+9}
\] |
[_quadrature] |
✓ |
0.584 |
|
|
\[
{}y^{\prime } = \frac {10}{x^{2}+1}
\] |
[_quadrature] |
✓ |
1.008 |
|
|
\[
{}y^{\prime } = \cos \left (2 x \right )
\] |
[_quadrature] |
✓ |
0.328 |
|
|
\[
{}y^{\prime } = \frac {1}{\sqrt {-x^{2}+1}}
\] |
[_quadrature] |
✓ |
0.987 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-x}
\] |
[_quadrature] |
✓ |
0.314 |
|
|
\[
{}y^{\prime } = -\sin \left (x \right )-y
\] |
[[_linear, ‘class A‘]] |
✓ |
2.381 |
|
|
\[
{}y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.288 |
|
|
\[
{}y^{\prime } = -\sin \left (x \right )+y
\] |
[[_linear, ‘class A‘]] |
✓ |
2.319 |
|
|
\[
{}y^{\prime } = x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.228 |
|
|
\[
{}y^{\prime } = 1-x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.467 |
|
|
\[
{}y^{\prime } = 1+x -y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.973 |
|
|
\[
{}y^{\prime } = x^{2}-y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.248 |
|
|
\[
{}y^{\prime } = -2+x^{2}-y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.262 |
|
|
\[
{}y^{\prime } = 2 x^{2} y^{2}
\] |
[_separable] |
✓ |
3.903 |
|
|
\[
{}y^{\prime } = x \ln \left (y\right )
\] |
[_separable] |
✓ |
2.210 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
0.536 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
0.556 |
|
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
9.345 |
|
|
\[
{}y y^{\prime } = x -1
\] |
[_separable] |
✓ |
6.146 |
|
|
\[
{}y^{\prime } = \ln \left (1+y^{2}\right )
\] |
[_quadrature] |
✓ |
1.493 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.970 |
|
|
\[
{}2 y x +y^{\prime } = 0
\] |
[_separable] |
✓ |
2.140 |
|
|
\[
{}y^{\prime }+2 x y^{2} = 0
\] |
[_separable] |
✓ |
2.757 |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
2.433 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 4 y
\] |
[_separable] |
✓ |
2.555 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime } = \sqrt {1-y^{2}}
\] |
[_separable] |
✓ |
2.173 |
|
|
\[
{}y^{\prime } = 3 \sqrt {y x}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
11.918 |
|
|
\[
{}y^{\prime } = 4 \left (y x \right )^{{1}/{3}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
5.796 |
|
|
\[
{}y^{\prime } = 2 x \sec \left (y\right )
\] |
[_separable] |
✓ |
2.618 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 2 y
\] |
[_separable] |
✓ |
2.571 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \left (1+y\right )^{2}
\] |
[_separable] |
✓ |
3.116 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
4.335 |
|
|
\[
{}y y^{\prime } = x \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
3.053 |
|
|
\[
{}y^{\prime } = \frac {1+\sqrt {x}}{1+\sqrt {y}}
\] |
[_separable] |
✓ |
3.049 |
|
|
\[
{}y^{\prime } = \frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )}
\] |
[_separable] |
✓ |
3.071 |
|
|
\[
{}\left (x^{2}+1\right ) \tan \left (y\right ) y^{\prime } = x
\] |
[_separable] |
✓ |
3.307 |
|
|
\[
{}y^{\prime } = 1+x +y+y x
\] |
[_separable] |
✓ |
1.576 |
|
|
\[
{}x^{2} y^{\prime } = 1-x^{2}+y^{2}-x^{2} y^{2}
\] |
[_separable] |
✓ |
3.105 |
|
|
\[
{}y^{\prime } = y \,{\mathrm e}^{x}
\] |
[_separable] |
✓ |
2.575 |
|
|
\[
{}y^{\prime } = 3 x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
3.996 |
|
|
\[
{}2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}}
\] |
[_separable] |
✓ |
3.204 |
|
|
\[
{}y^{\prime } = -y+4 x^{3} y
\] |
[_separable] |
✓ |
2.785 |
|
|
\[
{}1+y^{\prime } = 2 y
\] |
[_quadrature] |
✓ |
1.230 |
|
|
\[
{}\tan \left (x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
3.204 |
|
|
\[
{}y^{\prime } x -y = 2 x^{2} y
\] |
[_separable] |
✓ |
2.708 |
|