|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\cot \left (x \right ) y^{\prime }+y = x
\] |
[_linear] |
✓ |
1.821 |
|
|
\[
{}\cot \left (x \right ) y^{\prime }+y = \tan \left (x \right )
\] |
[_linear] |
✓ |
2.262 |
|
|
\[
{}y^{\prime } \tan \left (x \right )+y = \cot \left (x \right )
\] |
[_linear] |
✓ |
2.102 |
|
|
\[
{}y^{\prime } \tan \left (x \right ) = y-\cos \left (x \right )
\] |
[_linear] |
✓ |
2.821 |
|
|
\[
{}y^{\prime }+\cos \left (x \right ) y = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
1.807 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
2.848 |
|
|
\[
{}y^{\prime }+y \sin \left (x \right ) = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
1.921 |
|
|
\[
{}y^{\prime } \sin \left (x \right )+y = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
2.895 |
|
|
\[
{}\sqrt {x^{2}+1}\, y^{\prime }+y = 2 x
\] |
[_linear] |
✓ |
1.744 |
|
|
\[
{}\sqrt {x^{2}+1}\, y^{\prime }-y = 2 \sqrt {x^{2}+1}
\] |
[_linear] |
✓ |
1.895 |
|
|
\[
{}\sqrt {\left (x +a \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y = 0
\] |
[_linear] |
✓ |
2.346 |
|
|
\[
{}\sqrt {\left (x +a \right ) \left (x +b \right )}\, y^{\prime }+y = \sqrt {x +a}-\sqrt {x +b}
\] |
[_linear] |
✓ |
3.324 |
|
|
\[
{}3 y^{2} y^{\prime } = 2 x -1
\] |
[_separable] |
✓ |
2.133 |
|
|
\[
{}y^{\prime } = 6 x y^{2}
\] |
[_separable] |
✓ |
1.635 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{y} \sin \left (x \right )
\] |
[_separable] |
✓ |
1.586 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
1.885 |
|
|
\[
{}y^{\prime } = x \sec \left (y\right )
\] |
[_separable] |
✓ |
1.294 |
|
|
\[
{}y^{\prime } = 3 \cos \left (y\right )^{2}
\] |
[_quadrature] |
✓ |
0.879 |
|
|
\[
{}y^{\prime } x = y
\] |
[_separable] |
✓ |
1.426 |
|
|
\[
{}\left (1-x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
1.406 |
|
|
\[
{}y^{\prime } = \frac {4 x y}{x^{2}+1}
\] |
[_separable] |
✓ |
1.210 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x^{2}-1}
\] |
[_separable] |
✓ |
1.292 |
|
|
\[
{}-y^{2}+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.729 |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
2.417 |
|
|
\[
{}\cot \left (x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
1.989 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-2 y}
\] |
[_separable] |
✓ |
1.716 |
|
|
\[
{}y^{\prime }-2 x y = 2 x
\] |
[_separable] |
✓ |
1.428 |
|
|
\[
{}y^{\prime } x = x y+y
\] |
[_separable] |
✓ |
1.498 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime } = 3 x^{2} \tan \left (x \right )
\] |
[_quadrature] |
✓ |
1.074 |
|
|
\[
{}x \cos \left (y\right ) y^{\prime } = 1+\sin \left (y\right )
\] |
[_separable] |
✓ |
2.999 |
|
|
\[
{}y^{\prime } x = 2 y \left (-1+y\right )
\] |
[_separable] |
✓ |
2.319 |
|
|
\[
{}2 y^{\prime } x = 1-y^{2}
\] |
[_separable] |
✓ |
1.842 |
|
|
\[
{}\left (1-x \right ) y^{\prime } = x y
\] |
[_separable] |
✓ |
1.336 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime } = \left (x^{2}+1\right ) y
\] |
[_separable] |
✓ |
1.653 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.090 |
|
|
\[
{}{\mathrm e}^{y} y^{\prime }+2 x = 2 x \,{\mathrm e}^{y}
\] |
[_separable] |
✓ |
1.561 |
|
|
\[
{}y \,{\mathrm e}^{2 x} y^{\prime }+2 x = 0
\] |
[_separable] |
✓ |
2.144 |
|
|
\[
{}x y^{\prime } y = \sqrt {y^{2}-9}
\] |
[_separable] |
✓ |
4.216 |
|
|
\[
{}\left (x +y-1\right ) y^{\prime } = x -y+1
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.871 |
|
|
\[
{}x y^{\prime } y = 2 x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.255 |
|
|
\[
{}x^{2}-y^{2}+x y^{\prime } y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.328 |
|
|
\[
{}x^{2} y^{\prime }-2 x y-2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.270 |
|
|
\[
{}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.804 |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.866 |
|
|
\[
{}y^{\prime } x = y+2 \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
1.661 |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.506 |
|
|
\[
{}y^{\prime } = \sin \left (x -y+1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
6.173 |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x -y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.564 |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x +y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.962 |
|
|
\[
{}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.483 |
|
|
\[
{}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
43.641 |
|
|
\[
{}y-x^{3}+\left (y^{3}+x \right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.288 |
|
|
\[
{}2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime }
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.650 |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.814 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.938 |
|
|
\[
{}\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right )
\] |
[_exact] |
✓ |
31.104 |
|
|
\[
{}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
1.598 |
|
|
\[
{}1+y+\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.460 |
|
|
\[
{}2 x y^{3}+\cos \left (x \right ) y+\left (3 x^{2} y^{2}+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
43.661 |
|
|
\[
{}1 = \frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}}
\] |
[_exact, _rational, _Riccati] |
✓ |
1.580 |
|
|
\[
{}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.497 |
|
|
\[
{}x y-1+\left (x^{2}-x y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.315 |
|
|
\[
{}\left (x +3 y^{4} x^{3}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
12.710 |
|
|
\[
{}\left (x -1-y^{2}\right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.555 |
|
|
\[
{}y-\left (x +x y^{3}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.534 |
|
|
\[
{}y^{\prime } x = x^{5}+x^{3} y^{2}+y
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.235 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y-x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.489 |
|
|
\[
{}y^{\prime } x = y+x^{2}+9 y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.375 |
|
|
\[
{}y^{\prime } x -3 y = x^{4}
\] |
[_linear] |
✓ |
1.514 |
|
|
\[
{}y^{\prime }+y = \frac {1}{{\mathrm e}^{2 x}+1}
\] |
[_linear] |
✓ |
1.836 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = \cot \left (x \right )
\] |
[_linear] |
✓ |
1.717 |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.553 |
|
|
\[
{}y^{\prime }+\cot \left (x \right ) y = 2 x \csc \left (x \right )
\] |
[_linear] |
✓ |
1.784 |
|
|
\[
{}2 y-x^{3} = y^{\prime } x
\] |
[_linear] |
✓ |
1.536 |
|
|
\[
{}\left (1-x y\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.514 |
|
|
\[
{}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.495 |
|
|
\[
{}y^{\prime } x = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
9.765 |
|
|
\[
{}y^{2} = \left (x^{3}-x y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.954 |
|
|
\[
{}x^{2} y^{3}+y = \left (x^{3} y^{2}-x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.686 |
|
|
\[
{}y^{\prime } x +y = x \cos \left (x \right )
\] |
[_linear] |
✓ |
1.323 |
|
|
\[
{}\left (x y-x^{2}\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
108.188 |
|
|
\[
{}\left ({\mathrm e}^{x}-3 x^{2} y^{2}\right ) y^{\prime }+y \,{\mathrm e}^{x} = 2 x y^{3}
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.130 |
|
|
\[
{}y+x^{2} = y^{\prime } x
\] |
[_linear] |
✓ |
1.192 |
|
|
\[
{}y^{\prime } x +y = x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.415 |
|
|
\[
{}6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.909 |
|
|
\[
{}\cos \left (x +y\right )-x \sin \left (x +y\right ) = x \sin \left (x +y\right ) y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
3.251 |
|
|
\[
{}y^{2} {\mathrm e}^{x y}+\cos \left (x \right )+\left ({\mathrm e}^{x y}+x y \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
36.130 |
|
|
\[
{}y^{\prime } \ln \left (x -y\right ) = 1+\ln \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
1.803 |
|
|
\[
{}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
1.408 |
|
|
\[
{}y^{2}-3 x y-2 x^{2} = \left (x^{2}-x y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.571 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{3}
\] |
[_linear] |
✓ |
1.600 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )-y \sin \left (x y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )-x \sin \left (x y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
41.731 |
|
|
\[
{}\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 2 x y-{\mathrm e}^{y}-x
\] |
[_exact] |
✓ |
1.901 |
|
|
\[
{}{\mathrm e}^{x} \left (x +1\right ) = \left (x \,{\mathrm e}^{x}-{\mathrm e}^{y} y\right ) y^{\prime }
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.006 |
|
|
\[
{}x^{2} y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
1.590 |
|
|
\[
{}x +y+\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.348 |
|
|
\[
{}\ln \left (x \right ) y^{\prime }+\frac {x +y}{x} = 0
\] |
[_linear] |
✓ |
1.259 |
|
|
\[
{}\cos \left (y\right )-x \sin \left (y\right ) y^{\prime } = \sec \left (x \right )^{2}
\] |
[_exact] |
✓ |
42.246 |
|
|
\[
{}y \sin \left (\frac {x}{y}\right )+x \cos \left (\frac {x}{y}\right )-1+\left (x \sin \left (\frac {x}{y}\right )-\frac {x^{2} \cos \left (\frac {x}{y}\right )}{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
40.116 |
|
|
\[
{}\frac {x}{x^{2}+y^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{x^{2}+y^{2}}-\frac {1}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
221.105 |
|