|
# |
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 |
✓ |
0.608 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.389 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+y-6 z \\ y^{\prime }=10 x-4 y+12 z \\ z^{\prime }=2 x-y+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.507 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y+4 z \\ y^{\prime }=2 x+2 z \\ z^{\prime }=4 x+2 y+3 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.437 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y+z \\ y^{\prime }=-x-3 y-z \\ z^{\prime }=x+y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.437 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y+z \\ y^{\prime }=-3 x+2 y+3 z \\ z^{\prime }=x-y-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.336 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \\ z^{\prime }=2 h \\ h^{\prime }=-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.549 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y+z \\ y^{\prime }=-2 x+h \\ z^{\prime }=2 h \\ h^{\prime }=-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.566 |
|
|
\[
{}x^{\prime } = x \left (1-x\right )
\] |
[_quadrature] |
✓ |
1.883 |
|
|
\[
{}x^{\prime } = -x \left (1-x\right )
\] |
[_quadrature] |
✓ |
1.750 |
|
|
\[
{}x^{\prime } = x^{2}
\] |
[_quadrature] |
✓ |
1.278 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-\frac {\left (x_{1}^{2}+\sqrt {x_{1}^{2}+4 x_{2}^{2}}\right ) x_{1}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.067 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}+1 \\ x_{2}^{\prime }=2 x_{1}-x_{2}+5 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.891 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x^{3}-x y \\ y^{\prime }=2 y-y^{5}-y \,x^{4} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.069 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2}+y^{2}+1 \\ y^{\prime }=x^{2}-y^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.064 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2}+y^{2}-1 \\ y^{\prime }=2 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.054 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-6 x^{2}-2 x y \\ y^{\prime }=4 y-4 y^{2}-2 x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.059 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\tan \left (x+y\right ) \\ y^{\prime }=x+x^{3} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.036 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }={\mathrm e}^{y}-x \\ y^{\prime }={\mathrm e}^{x}+y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.054 |
|
|
\[
{}z^{\prime \prime }+z^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.617 |
|
|
\[
{}z^{\prime \prime }+z+z^{5} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
278.431 |
|
|
\[
{}z^{\prime \prime }+{\mathrm e}^{z^{2}} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.036 |
|
|
\[
{}z^{\prime \prime }+\frac {z}{1+z^{2}} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.191 |
|
|
\[
{}z^{\prime \prime }+z-2 z^{3} = 0
\] |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.250 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-5 x_{1}+x_{2} \\ x_{2}^{\prime }=x_{1}-5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.421 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2} \\ x_{2}^{\prime }=8 x_{1}-6 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.428 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-x_{2} \\ x_{2}^{\prime }=-2 x_{1}+5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.421 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}-6 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.377 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=-8 x_{1}+4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.623 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.421 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{2} \\ x_{2}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.719 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.493 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2} \\ x_{2}^{\prime }=-5 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.475 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{2} \\ x_{2}^{\prime }=-9 x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.460 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.059 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.171 |
|
|
\[
{}y^{\prime \prime }-\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.777 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.074 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+\left (1+\lambda \right ) y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.869 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.027 |
|
|
\[
{}x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.730 |
|
|
\[
{}x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.601 |
|
|
\[
{}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.128 |
|
|
\[
{}y+y^{\prime } x = 0
\] |
[_separable] |
✓ |
2.115 |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
1.628 |
|
|
\[
{}x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.027 |
|
|
\[
{}\sqrt {-x^{2}+1}+\sqrt {1-y^{2}}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
2.000 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-1+y = 0
\] |
[_separable] |
✓ |
1.822 |
|
|
\[
{}y^{\prime } \tan \left (x \right )-y = 1
\] |
[_separable] |
✓ |
1.824 |
|
|
\[
{}y+3+\cot \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.964 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
3.563 |
|
|
\[
{}x^{\prime } = 1-\sin \left (2 t \right )
\] |
[_quadrature] |
✓ |
0.557 |
|
|
\[
{}y+y^{\prime } x = y^{2}
\] |
[_separable] |
✓ |
2.064 |
|
|
\[
{}\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.564 |
|
|
\[
{}\sec \left (x \right ) \cos \left (y\right )^{2} = \cos \left (x \right ) \sin \left (y\right ) y^{\prime }
\] |
[_separable] |
✓ |
8.467 |
|
|
\[
{}y+y^{\prime } x = x y \left (y^{\prime }-1\right )
\] |
[_separable] |
✓ |
1.433 |
|
|
\[
{}x y+\sqrt {x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
1.984 |
|
|
\[
{}y = x y+x^{2} y^{\prime }
\] |
[_separable] |
✓ |
1.847 |
|
|
\[
{}\tan \left (x \right ) \sin \left (x \right )^{2}+\cos \left (x \right )^{2} \cot \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
5.505 |
|
|
\[
{}y^{2}+y y^{\prime }+x^{2} y y^{\prime }-1 = 0
\] |
[_separable] |
✓ |
3.986 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.919 |
|
|
\[
{}y^{\prime } x +2 y = 0
\] |
[_separable] |
✓ |
2.703 |
|
|
\[
{}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.167 |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
3.629 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{y}
\] |
[_quadrature] |
✓ |
1.611 |
|
|
\[
{}{\mathrm e}^{y} \left (y^{\prime }+1\right ) = 1
\] |
[_quadrature] |
✓ |
1.989 |
|
|
\[
{}1+y^{2} = \frac {y^{\prime }}{x^{3} \left (x -1\right )}
\] |
[_separable] |
✓ |
3.259 |
|
|
\[
{}x^{2}+3 y^{\prime } x = y^{3}+2 y
\] |
[_rational, _Abel] |
✓ |
14.246 |
|
|
\[
{}\left (x^{2}+x +1\right ) y^{\prime } = y^{2}+2 y+5
\] |
[_separable] |
✓ |
4.858 |
|
|
\[
{}\left (x^{2}-2 x -8\right ) y^{\prime } = y^{2}+y-2
\] |
[_separable] |
✓ |
4.393 |
|
|
\[
{}x +y = y^{\prime } x
\] |
[_linear] |
✓ |
1.481 |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.618 |
|
|
\[
{}y^{\prime } x -y = \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.696 |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.588 |
|
|
\[
{}y^{\prime } x -y = \sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
54.954 |
|
|
\[
{}x +y y^{\prime } = 2 y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.290 |
|
|
\[
{}y^{\prime } x -y+\sqrt {y^{2}-x^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.442 |
|
|
\[
{}x^{2}+y^{2} = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.477 |
|
|
\[
{}\left (x y-x^{2}\right ) y^{\prime }-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
37.523 |
|
|
\[
{}y+y^{\prime } x = 2 \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.002 |
|
|
\[
{}x +y+\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.676 |
|
|
\[
{}y \left (x^{2}-x y+y^{2}\right )+x y^{\prime } \left (x^{2}+x y+y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
53.445 |
|
|
\[
{}y^{\prime } x -y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.814 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\cosh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.115 |
|
|
\[
{}x^{2}+y^{2} = 2 x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
9.719 |
|
|
\[
{}\left (\frac {x}{y}+\frac {y}{x}\right ) y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.609 |
|
|
\[
{}x \,{\mathrm e}^{\frac {y}{x}}+y = y^{\prime } x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.514 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.581 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.701 |
|
|
\[
{}\left (3 x y-2 x^{2}\right ) y^{\prime } = 2 y^{2}-x y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
47.150 |
|
|
\[
{}y^{\prime } = \frac {y}{x -k \sqrt {x^{2}+y^{2}}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
78.126 |
|
|
\[
{}y^{2} \left (y y^{\prime }-x \right )+x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
15.394 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tanh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
7.265 |
|
|
\[
{}x +y-\left (x -y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.434 |
|
|
\[
{}x +\left (x -2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
4.199 |
|
|
\[
{}2 x -y+1+\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.615 |
|
|
\[
{}x -y+2+\left (x +y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.601 |
|
|
\[
{}x -y+\left (y-x +1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.013 |
|
|
\[
{}y^{\prime } = \frac {x +y-1}{x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.443 |
|
|
\[
{}x +y+\left (2 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.747 |
|