|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+3 y \\ y^{\prime }=-x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.567 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.320 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+y-6 z \\ y^{\prime }=10 x-4 y+12 z \\ z^{\prime }=2 x-y+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.609 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y+4 z \\ y^{\prime }=2 x+2 z \\ z^{\prime }=4 x+2 y+3 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.473 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y+z \\ y^{\prime }=-x-3 y-z \\ z^{\prime }=x+y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.510 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y+z \\ y^{\prime }=-3 x+2 y+3 z \\ z^{\prime }=x-y-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.409 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \\ z^{\prime }=2 h \\ h^{\prime }=-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.580 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y+z \\ y^{\prime }=-2 x+h \\ z^{\prime }=2 h \\ h^{\prime }=-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.644 |
|
|
\[
{}x^{\prime } = x \left (1-x\right )
\] |
[_quadrature] |
✓ |
1.020 |
|
|
\[
{}x^{\prime } = -x \left (1-x\right )
\] |
[_quadrature] |
✓ |
0.957 |
|
|
\[
{}x^{\prime } = x^{2}
\] |
[_quadrature] |
✓ |
1.430 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-\frac {\left (x_{1}^{2}+\sqrt {x_{1}^{2}+4 x_{2}^{2}}\right ) x_{1}}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.058 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}+1 \\ x_{2}^{\prime }=2 x_{1}-x_{2}+5 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.899 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x^{3}-x y \\ y^{\prime }=2 y-y^{5}-y \,x^{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.062 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2}+y^{2}+1 \\ y^{\prime }=x^{2}-y^{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.050 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2}+y^{2}-1 \\ y^{\prime }=2 x y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.057 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-6 x^{2}-2 x y \\ y^{\prime }=4 y-4 y^{2}-2 x y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.055 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\tan \left (x+y\right ) \\ y^{\prime }=x+x^{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.050 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }={\mathrm e}^{y}-x \\ y^{\prime }={\mathrm e}^{x}+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.053 |
|
|
\[
{}z^{\prime \prime }+z^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
4.395 |
|
|
\[
{}z^{\prime \prime }+z+z^{5} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
708.952 |
|
|
\[
{}z^{\prime \prime }+{\mathrm e}^{z^{2}} = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.682 |
|
|
\[
{}z^{\prime \prime }+\frac {z}{1+z^{2}} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.195 |
|
|
\[
{}z^{\prime \prime }+z-2 z^{3} = 0
\] |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
5.505 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-5 x_{1}+x_{2} \\ x_{2}^{\prime }=x_{1}-5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.365 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2} \\ x_{2}^{\prime }=8 x_{1}-6 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.420 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-x_{2} \\ x_{2}^{\prime }=-2 x_{1}+5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.408 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}-6 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.313 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=-8 x_{1}+4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.610 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.420 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{2} \\ x_{2}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.732 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.506 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2} \\ x_{2}^{\prime }=-5 x_{1}-2 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.427 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{2} \\ x_{2}^{\prime }=-9 x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.405 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.298 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.397 |
|
|
\[
{}y^{\prime \prime }-\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.897 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.310 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+\left (1+\lambda \right ) y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.623 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.385 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
1.191 |
|
|
\[
{}x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.762 |
|
|
\[
{}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.825 |
|
|
\[
{}y^{\prime } x +y = 0
\] |
[_separable] |
✓ |
1.442 |
|
|
\[
{}y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
1.123 |
|
|
\[
{}x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.621 |
|
|
\[
{}\sqrt {-x^{2}+1}+\sqrt {1-y^{2}}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
2.238 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-1+y = 0
\] |
[_separable] |
✓ |
1.415 |
|
|
\[
{}y^{\prime } \tan \left (x \right )-y = 1
\] |
[_separable] |
✓ |
1.525 |
|
|
\[
{}y+3+\cot \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.049 |
|
|
\[
{}y^{\prime } = \frac {x}{y}
\] |
[_separable] |
✓ |
3.480 |
|
|
\[
{}x^{\prime } = 1-\sin \left (2 t \right )
\] |
[_quadrature] |
✓ |
0.400 |
|
|
\[
{}y^{\prime } x +y = y^{2}
\] |
[_separable] |
✓ |
1.527 |
|
|
\[
{}\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.567 |
|
|
\[
{}\sec \left (x \right ) \cos \left (y\right )^{2} = \cos \left (x \right ) \sin \left (y\right ) y^{\prime }
\] |
[_separable] |
✓ |
7.840 |
|
|
\[
{}y^{\prime } x +y = x y \left (y^{\prime }-1\right )
\] |
[_separable] |
✓ |
1.477 |
|
|
\[
{}x y+\sqrt {x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
1.589 |
|
|
\[
{}y = x y+x^{2} y^{\prime }
\] |
[_separable] |
✓ |
1.514 |
|
|
\[
{}\tan \left (x \right ) \sin \left (x \right )^{2}+\cos \left (x \right )^{2} \cot \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
6.332 |
|
|
\[
{}y^{2}+y y^{\prime }+x^{2} y y^{\prime }-1 = 0
\] |
[_separable] |
✓ |
4.025 |
|
|
\[
{}y^{\prime } = \frac {y}{x}
\] |
[_separable] |
✓ |
1.532 |
|
|
\[
{}y^{\prime } x +2 y = 0
\] |
[_separable] |
✓ |
1.776 |
|
|
\[
{}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.174 |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = 0
\] |
[_separable] |
✓ |
2.666 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{y}
\] |
[_quadrature] |
✓ |
1.259 |
|
|
\[
{}{\mathrm e}^{y} \left (y^{\prime }+1\right ) = 1
\] |
[_quadrature] |
✓ |
1.484 |
|
|
\[
{}1+y^{2} = \frac {y^{\prime }}{x^{3} \left (x -1\right )}
\] |
[_separable] |
✓ |
3.281 |
|
|
\[
{}x^{2}+3 y^{\prime } x = y^{3}+2 y
\] |
[_rational, _Abel] |
✓ |
17.620 |
|
|
\[
{}\left (x^{2}+x +1\right ) y^{\prime } = y^{2}+2 y+5
\] |
[_separable] |
✓ |
4.462 |
|
|
\[
{}\left (x^{2}-2 x -8\right ) y^{\prime } = y^{2}+y-2
\] |
[_separable] |
✓ |
3.885 |
|
|
\[
{}x +y = y^{\prime } x
\] |
[_linear] |
✓ |
1.291 |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.431 |
|
|
\[
{}y^{\prime } x -y = \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.287 |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.678 |
|
|
\[
{}y^{\prime } x -y = \sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
119.919 |
|
|
\[
{}y y^{\prime }+x = 2 y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.209 |
|
|
\[
{}y^{\prime } x -y+\sqrt {y^{2}-x^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.366 |
|
|
\[
{}x^{2}+y^{2} = x y^{\prime } y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.244 |
|
|
\[
{}\left (x y-x^{2}\right ) y^{\prime }-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
77.657 |
|
|
\[
{}y^{\prime } x +y = 2 \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
21.532 |
|
|
\[
{}x +y+\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.974 |
|
|
\[
{}y \left (x^{2}-x y+y^{2}\right )+x y^{\prime } \left (x^{2}+x y+y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
173.829 |
|
|
\[
{}y^{\prime } x -y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.745 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\cosh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.864 |
|
|
\[
{}x^{2}+y^{2} = 2 x y^{\prime } y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
6.083 |
|
|
\[
{}\left (\frac {x}{y}+\frac {y}{x}\right ) y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.426 |
|
|
\[
{}{\mathrm e}^{\frac {y}{x}} x +y = y^{\prime } x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.414 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.523 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.595 |
|
|
\[
{}\left (3 x y-2 x^{2}\right ) y^{\prime } = 2 y^{2}-x y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
9.353 |
|
|
\[
{}y^{\prime } = \frac {y}{x -k \sqrt {x^{2}+y^{2}}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
140.811 |
|
|
\[
{}y^{2} \left (y y^{\prime }-x \right )+x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
27.041 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tanh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
106.757 |
|
|
\[
{}x +y-\left (x -y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.428 |
|
|
\[
{}x +\left (x -2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
2.829 |
|
|
\[
{}2 x -y+1+\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.775 |
|
|
\[
{}x -y+2+\left (x +y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.557 |
|
|
\[
{}x -y+\left (y-x +1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.562 |
|
|
\[
{}y^{\prime } = \frac {x +y-1}{x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.411 |
|
|
\[
{}x +y+\left (2 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.977 |
|