|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.572 |
|
|
\[
{}y = y^{\prime }+\frac {{y^{\prime }}^{2}}{2}
\] |
[_quadrature] |
✓ |
1.641 |
|
|
\[
{}\left (y-y^{\prime } x \right )^{2} = 1+{y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.771 |
|
|
\[
{}-x +y = {y^{\prime }}^{2} \left (1-\frac {2 y^{\prime }}{3}\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
3.411 |
|
|
\[
{}x^{2} y^{\prime } = x \left (-1+y\right )+\left (-1+y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
2.960 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-x}
\] |
[_quadrature] |
✓ |
0.262 |
|
|
\[
{}y^{\prime } = 1-x^{5}+\sqrt {x}
\] |
[_quadrature] |
✓ |
0.247 |
|
|
\[
{}3 y-2 x +\left (3 x -2\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
8.534 |
|
|
\[
{}x^{2}+x -1+\left (2 y x +y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.897 |
|
|
\[
{}{\mathrm e}^{2 y}+\left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.073 |
|
|
\[
{}\left (x +1\right ) y^{\prime }-x^{2} y^{2} = 0
\] |
[_separable] |
✓ |
6.865 |
|
|
\[
{}y^{\prime } = \frac {y-2 x}{x}
\] |
[_linear] |
✓ |
2.970 |
|
|
\[
{}x^{3}+y^{3}-x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
33.394 |
|
|
\[
{}y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
0.896 |
|
|
\[
{}y^{\prime }+y = x^{2}+2
\] |
[[_linear, ‘class A‘]] |
✓ |
1.433 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = x
\] |
[_linear] |
✓ |
1.924 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -2 y}
\] |
[_separable] |
✓ |
9.530 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+y^{2}}{2 x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
3.481 |
|
|
\[
{}y^{\prime } x = x +y
\] |
[_linear] |
✓ |
6.933 |
|
|
\[
{}{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.605 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.625 |
|
|
\[
{}y^{\prime }-3 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.000 |
|
|
\[
{}y^{\prime } = x +\frac {1}{x}
\] |
[_quadrature] |
✓ |
0.409 |
|
|
\[
{}y^{\prime } x +2 y = \left (2+3 x \right ) {\mathrm e}^{3 x}
\] |
[_linear] |
✓ |
2.188 |
|
|
\[
{}2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }-3 \cos \left (3 x \right ) \cos \left (2 y\right ) = 0
\] |
[_separable] |
✓ |
12.901 |
|
|
\[
{}x y y^{\prime } = \left (x +1\right ) \left (1+y\right )
\] |
[_separable] |
✓ |
2.613 |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{y+2 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
59.710 |
|
|
\[
{}y^{\prime } = \frac {3 x -y+1}{3 y-x +5}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
38.352 |
|
|
\[
{}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1142.302 |
|
|
\[
{}x +\left (2-x +2 y\right ) y^{\prime } = x y \left (y^{\prime }-1\right )
\] |
[_quadrature] |
✓ |
0.468 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y \sin \left (x \right ) = 1
\] |
[_linear] |
✓ |
3.370 |
|
|
\[
{}\left (x +y^{2}\right ) y^{\prime }+y-x^{2} = 0
\] |
[_exact, _rational] |
✓ |
7.477 |
|
|
\[
{}y y^{\prime } = x
\] |
[_separable] |
✓ |
16.642 |
|
|
\[
{}y^{\prime }-y = x^{3}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.188 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = x
\] |
[_linear] |
✓ |
2.056 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = \tan \left (x \right )
\] |
[_linear] |
✓ |
7.391 |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = \cot \left (x \right )
\] |
[_linear] |
✓ |
2.095 |
|
|
\[
{}y^{\prime }+y \ln \left (x \right ) = x^{-x}
\] |
[_linear] |
✓ |
1.906 |
|
|
\[
{}y^{\prime } x +y = x
\] |
[_linear] |
✓ |
9.918 |
|
|
\[
{}y^{\prime } x -y = x^{3}
\] |
[_linear] |
✓ |
1.747 |
|
|
\[
{}y^{\prime } x +n y = x^{n}
\] |
[_linear] |
✓ |
3.109 |
|
|
\[
{}y^{\prime } x -n y = x^{n}
\] |
[_linear] |
✓ |
2.033 |
|
|
\[
{}\left (x^{3}+x \right ) y^{\prime }+y = x
\] |
[_linear] |
✓ |
10.565 |
|
|
\[
{}\cot \left (x \right ) y^{\prime }+y = x
\] |
[_linear] |
✓ |
2.813 |
|
|
\[
{}\cot \left (x \right ) y^{\prime }+y = \tan \left (x \right )
\] |
[_linear] |
✓ |
8.546 |
|
|
\[
{}\tan \left (x \right ) y^{\prime }+y = \cot \left (x \right )
\] |
[_linear] |
✓ |
3.503 |
|
|
\[
{}\tan \left (x \right ) y^{\prime } = y-\cos \left (x \right )
\] |
[_linear] |
✓ |
4.627 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
7.910 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
5.225 |
|
|
\[
{}y^{\prime }+y \sin \left (x \right ) = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
2.631 |
|
|
\[
{}\sin \left (x \right ) y^{\prime }+y = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
10.145 |
|
|
\[
{}\sqrt {x^{2}+1}\, y^{\prime }+y = 2 x
\] |
[_linear] |
✓ |
2.216 |
|
|
\[
{}\sqrt {x^{2}+1}\, y^{\prime }-y = 2 \sqrt {x^{2}+1}
\] |
[_linear] |
✓ |
3.347 |
|
|
\[
{}\sqrt {\left (x +a \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y = 0
\] |
[_linear] |
✓ |
10.125 |
|
|
\[
{}\sqrt {\left (x +a \right ) \left (x +b \right )}\, y^{\prime }+y = \sqrt {x +a}-\sqrt {x +b}
\] |
[_linear] |
✓ |
5.388 |
|
|
\[
{}3 y^{2} y^{\prime } = 2 x -1
\] |
[_separable] |
✓ |
9.519 |
|
|
\[
{}y^{\prime } = 6 x y^{2}
\] |
[_separable] |
✓ |
4.165 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{y} \sin \left (x \right )
\] |
[_separable] |
✓ |
2.381 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
8.340 |
|
|
\[
{}y^{\prime } = x \sec \left (y\right )
\] |
[_separable] |
✓ |
2.442 |
|
|
\[
{}y^{\prime } = 3 \cos \left (y\right )^{2}
\] |
[_quadrature] |
✓ |
0.816 |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
2.298 |
|
|
\[
{}\left (1-x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
8.752 |
|
|
\[
{}y^{\prime } = \frac {4 x y}{x^{2}+1}
\] |
[_separable] |
✓ |
2.667 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x^{2}-1}
\] |
[_separable] |
✓ |
7.915 |
|
|
\[
{}x^{2} y^{\prime }-y^{2} = 0
\] |
[_separable] |
✓ |
6.587 |
|
|
\[
{}y^{\prime }+2 y x = 0
\] |
[_separable] |
✓ |
7.786 |
|
|
\[
{}\cot \left (x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
5.174 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-2 y}
\] |
[_separable] |
✓ |
7.954 |
|
|
\[
{}y^{\prime }-2 y x = 2 x
\] |
[_separable] |
✓ |
2.197 |
|
|
\[
{}y^{\prime } x = y x +y
\] |
[_separable] |
✓ |
2.350 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime } = 3 x^{2} \tan \left (x \right )
\] |
[_quadrature] |
✓ |
1.116 |
|
|
\[
{}x \cos \left (y\right ) y^{\prime } = 1+\sin \left (y\right )
\] |
[_separable] |
✓ |
12.432 |
|
|
\[
{}y^{\prime } x = 2 y \left (-1+y\right )
\] |
[_separable] |
✓ |
12.638 |
|
|
\[
{}2 y^{\prime } x = 1-y^{2}
\] |
[_separable] |
✓ |
2.796 |
|
|
\[
{}\left (1-x \right ) y^{\prime } = y x
\] |
[_separable] |
✓ |
7.570 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime } = \left (x^{2}+1\right ) y
\] |
[_separable] |
✓ |
3.124 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.678 |
|
|
\[
{}{\mathrm e}^{y} y^{\prime }+2 x = 2 x \,{\mathrm e}^{y}
\] |
[_separable] |
✓ |
7.790 |
|
|
\[
{}y \,{\mathrm e}^{2 x} y^{\prime }+2 x = 0
\] |
[_separable] |
✓ |
2.242 |
|
|
\[
{}x y y^{\prime } = \sqrt {y^{2}-9}
\] |
[_separable] |
✓ |
19.863 |
|
|
\[
{}\left (x +y-1\right ) y^{\prime } = x -y+1
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
14.070 |
|
|
\[
{}x y y^{\prime } = 2 x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
30.214 |
|
|
\[
{}x^{2}-y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
22.807 |
|
|
\[
{}x^{2} y^{\prime }-2 y x -2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
11.980 |
|
|
\[
{}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+y x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
133.995 |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
32.976 |
|
|
\[
{}y^{\prime } x = y+2 \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
4.358 |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
7.922 |
|
|
\[
{}y^{\prime } = \sin \left (x -y+1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
24.694 |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x -y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.004 |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x +y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.728 |
|
|
\[
{}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.193 |
|
|
\[
{}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
82.118 |
|
|
\[
{}y-x^{3}+\left (x +y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
2.168 |
|
|
\[
{}2 y^{2}-4 x +5 = \left (4-2 y+4 y x \right ) y^{\prime }
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.909 |
|
|
\[
{}y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
10.041 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
7.773 |
|
|
\[
{}\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right )
\] |
[_exact] |
✓ |
86.263 |
|
|
\[
{}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
10.208 |
|