|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+3 y \\ y^{\prime }=y-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.589 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.439 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+y-6 z \\ y^{\prime }=10 x-4 y+12 z \\ z^{\prime }=2 x-y+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.496 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y+4 z \\ y^{\prime }=2 x+2 z \\ z^{\prime }=4 x+2 y+3 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.410 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y+z \\ y^{\prime }=-x-3 y-z \\ z^{\prime }=x+y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.412 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y+z \\ y^{\prime }=-3 x+2 y+3 z \\ z^{\prime }=x-y-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.371 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \\ z^{\prime }=2 h \\ h^{\prime }=-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.541 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y+z \\ y^{\prime }=-2 x+h \\ z^{\prime }=2 h \\ h^{\prime }=-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.637 |
|
|
\[
{}x^{\prime } = x \left (1-x\right )
\] |
[_quadrature] |
✓ |
2.268 |
|
|
\[
{}x^{\prime } = -x \left (1-x\right )
\] |
[_quadrature] |
✓ |
1.965 |
|
|
\[
{}x^{\prime } = x^{2}
\] |
[_quadrature] |
✓ |
1.915 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-\frac {\left (x_{1}^{2}+\sqrt {x_{1}^{2}+4 x_{2}^{2}}\right ) x_{1}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.033 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}+1 \\ x_{2}^{\prime }=2 x_{1}-x_{2}+5 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.956 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x^{3}-x y \\ y^{\prime }=2 y-y^{5}-y \,x^{4} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.041 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2}+y^{2}+1 \\ y^{\prime }=x^{2}-y^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.037 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2}+y^{2}-1 \\ y^{\prime }=2 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.028 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-6 x^{2}-2 x y \\ y^{\prime }=4 y-4 y^{2}-2 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.035 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\tan \left (x+y\right ) \\ y^{\prime }=x+x^{3} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.031 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }={\mathrm e}^{y}-x \\ y^{\prime }={\mathrm e}^{x}+y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.030 |
|
|
\[
{}z^{\prime \prime }+z^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
4.279 |
|
|
\[
{}z^{\prime \prime }+z+z^{5} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
403.913 |
|
|
\[
{}z^{\prime \prime }+{\mathrm e}^{z^{2}} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.466 |
|
|
\[
{}z^{\prime \prime }+\frac {z}{1+z^{2}} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.232 |
|
|
\[
{}z^{\prime \prime }+z-2 z^{3} = 0
\] |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
4.536 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-5 x_{1}+x_{2} \\ x_{2}^{\prime }=x_{1}-5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.448 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2} \\ x_{2}^{\prime }=8 x_{1}-6 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.474 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-x_{2} \\ x_{2}^{\prime }=-2 x_{1}+5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.474 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}-6 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.437 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=-8 x_{1}+4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.612 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.464 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{2} \\ x_{2}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.796 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.563 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2} \\ x_{2}^{\prime }=-5 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.522 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{2} \\ x_{2}^{\prime }=-9 x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.506 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.028 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.357 |
|
|
\[
{}y^{\prime \prime }-\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.681 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.076 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+\left (1+\lambda \right ) y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.716 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.028 |
|
|
\[
{}x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.649 |
|
|
\[
{}x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
4.246 |
|
|
\[
{}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.266 |
|
|
\[
{}y+x y^{\prime } = 0
\] |
[_separable] |
✓ |
2.161 |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
1.642 |
|
|
\[
{}x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.738 |
|
|
\[
{}\sqrt {-x^{2}+1}+\sqrt {1-y^{2}}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
2.102 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-1+y = 0
\] |
[_separable] |
✓ |
2.017 |
|
|
\[
{}y^{\prime } \tan \left (x \right )-y = 1
\] |
[_separable] |
✓ |
1.847 |
|
|
\[
{}y+3+\cot \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.204 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
4.471 |
|
|
\[
{}x^{\prime } = 1-\sin \left (2 t \right )
\] |
[_quadrature] |
✓ |
0.603 |
|
|
\[
{}y+x y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
2.241 |
|
|
\[
{}\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.850 |
|
|
\[
{}\sec \left (x \right ) \cos \left (y\right )^{2} = \cos \left (x \right ) \sin \left (y\right ) y^{\prime }
\] |
[_separable] |
✓ |
7.589 |
|
|
\[
{}y+x y^{\prime } = x y \left (y^{\prime }-1\right )
\] |
[_separable] |
✓ |
1.465 |
|
|
\[
{}x y+\sqrt {x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
2.024 |
|
|
\[
{}y = x y+x^{2} y^{\prime }
\] |
[_separable] |
✓ |
1.884 |
|
|
\[
{}\tan \left (x \right ) \sin \left (x \right )^{2}+\cos \left (x \right )^{2} \cot \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
5.758 |
|
|
\[
{}y^{2}+y y^{\prime }+x^{2} y y^{\prime }-1 = 0
\] |
[_separable] |
✓ |
4.578 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
2.010 |
|
|
\[
{}x y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
2.636 |
|
|
\[
{}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.429 |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
3.558 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{y}
\] |
[_quadrature] |
✓ |
2.233 |
|
|
\[
{}{\mathrm e}^{y} \left (y^{\prime }+1\right ) = 1
\] |
[_quadrature] |
✓ |
2.632 |
|
|
\[
{}1+y^{2} = \frac {y^{\prime }}{x^{3} \left (-1+x \right )}
\] |
[_separable] |
✓ |
3.070 |
|
|
\[
{}x^{2}+3 x y^{\prime } = y^{3}+2 y
\] |
[_rational, _Abel] |
✓ |
15.955 |
|
|
\[
{}\left (x^{2}+x +1\right ) y^{\prime } = y^{2}+2 y+5
\] |
[_separable] |
✓ |
5.608 |
|
|
\[
{}\left (x^{2}-2 x -8\right ) y^{\prime } = y^{2}+y-2
\] |
[_separable] |
✓ |
5.332 |
|
|
\[
{}x +y = x y^{\prime }
\] |
[_linear] |
✓ |
1.526 |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
38.231 |
|
|
\[
{}x y^{\prime }-y = \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.223 |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.404 |
|
|
\[
{}x y^{\prime }-y = \sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
90.042 |
|
|
\[
{}x +y y^{\prime } = 2 y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.454 |
|
|
\[
{}x y^{\prime }-y+\sqrt {y^{2}-x^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.025 |
|
|
\[
{}x^{2}+y^{2} = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.886 |
|
|
\[
{}\left (x y-x^{2}\right ) y^{\prime }-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
72.746 |
|
|
\[
{}y+x y^{\prime } = 2 \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
13.032 |
|
|
\[
{}x +y+\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.454 |
|
|
\[
{}y \left (x^{2}-x y+y^{2}\right )+x y^{\prime } \left (y^{2}+x y+x^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
108.773 |
|
|
\[
{}x y^{\prime }-y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.713 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\cosh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.157 |
|
|
\[
{}x^{2}+y^{2} = 2 x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
8.003 |
|
|
\[
{}\left (\frac {x}{y}+\frac {y}{x}\right ) y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
97.135 |
|
|
\[
{}x \,{\mathrm e}^{\frac {y}{x}}+y = x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.127 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.162 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.906 |
|
|
\[
{}\left (3 x y-2 x^{2}\right ) y^{\prime } = 2 y^{2}-x y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
92.096 |
|
|
\[
{}y^{\prime } = \frac {y}{x -k \sqrt {x^{2}+y^{2}}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
73.005 |
|
|
\[
{}y^{2} \left (y y^{\prime }-x \right )+x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
24.429 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tanh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
53.626 |
|
|
\[
{}x +y-\left (x -y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
36.931 |
|
|
\[
{}x +\left (x -2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
2.871 |
|
|
\[
{}2 x -y+1+\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.947 |
|
|
\[
{}x -y+2+\left (x +y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
36.651 |
|
|
\[
{}x -y+\left (y-x +1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.789 |
|
|
\[
{}y^{\prime } = \frac {x +y-1}{x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
36.879 |
|
|
\[
{}x +y+\left (2 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.855 |
|