|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\cot \left (x \right ) y^{\prime }+y = x
\] |
[_linear] |
✓ |
1.832 |
|
|
\[
{}\cot \left (x \right ) y^{\prime }+y = \tan \left (x \right )
\] |
[_linear] |
✓ |
2.214 |
|
|
\[
{}\tan \left (x \right ) y^{\prime }+y = \cot \left (x \right )
\] |
[_linear] |
✓ |
2.131 |
|
|
\[
{}\tan \left (x \right ) y^{\prime } = y-\cos \left (x \right )
\] |
[_linear] |
✓ |
2.726 |
|
|
\[
{}y^{\prime }+y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
2.022 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
3.125 |
|
|
\[
{}y^{\prime }+y \sin \left (x \right ) = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
1.995 |
|
|
\[
{}\sin \left (x \right ) y^{\prime }+y = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
3.104 |
|
|
\[
{}\sqrt {x^{2}+1}\, y^{\prime }+y = 2 x
\] |
[_linear] |
✓ |
1.806 |
|
|
\[
{}\sqrt {x^{2}+1}\, y^{\prime }-y = 2 \sqrt {x^{2}+1}
\] |
[_linear] |
✓ |
1.964 |
|
|
\[
{}\sqrt {\left (x +a \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y = 0
\] |
[_linear] |
✓ |
2.197 |
|
|
\[
{}\sqrt {\left (x +a \right ) \left (x +b \right )}\, y^{\prime }+y = \sqrt {x +a}-\sqrt {x +b}
\] |
[_linear] |
✓ |
3.120 |
|
|
\[
{}3 y^{2} y^{\prime } = 2 x -1
\] |
[_separable] |
✓ |
2.297 |
|
|
\[
{}y^{\prime } = 6 x y^{2}
\] |
[_separable] |
✓ |
2.140 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{y} \sin \left (x \right )
\] |
[_separable] |
✓ |
1.814 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
2.352 |
|
|
\[
{}y^{\prime } = x \sec \left (y\right )
\] |
[_separable] |
✓ |
1.381 |
|
|
\[
{}y^{\prime } = 3 \cos \left (y\right )^{2}
\] |
[_quadrature] |
✓ |
1.470 |
|
|
\[
{}x y^{\prime } = y
\] |
[_separable] |
✓ |
1.597 |
|
|
\[
{}\left (1-x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
2.006 |
|
|
\[
{}y^{\prime } = \frac {4 x y}{x^{2}+1}
\] |
[_separable] |
✓ |
1.698 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x^{2}-1}
\] |
[_separable] |
✓ |
1.726 |
|
|
\[
{}x^{2} y^{\prime }-y^{2} = 0
\] |
[_separable] |
✓ |
3.608 |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
2.799 |
|
|
\[
{}\cot \left (x \right ) y^{\prime } = y
\] |
[_separable] |
✓ |
2.450 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-2 y}
\] |
[_separable] |
✓ |
2.252 |
|
|
\[
{}y^{\prime }-2 x y = 2 x
\] |
[_separable] |
✓ |
1.954 |
|
|
\[
{}x y^{\prime } = x y+y
\] |
[_separable] |
✓ |
2.125 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime } = 3 x^{2} \tan \left (x \right )
\] |
[_quadrature] |
✓ |
0.991 |
|
|
\[
{}x \cos \left (y\right ) y^{\prime } = 1+\sin \left (y\right )
\] |
[_separable] |
✓ |
3.590 |
|
|
\[
{}x y^{\prime } = 2 y \left (y-1\right )
\] |
[_separable] |
✓ |
3.017 |
|
|
\[
{}2 x y^{\prime } = 1-y^{2}
\] |
[_separable] |
✓ |
2.355 |
|
|
\[
{}\left (1-x \right ) y^{\prime } = x y
\] |
[_separable] |
✓ |
1.755 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime } = \left (x^{2}+1\right ) y
\] |
[_separable] |
✓ |
2.088 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.350 |
|
|
\[
{}{\mathrm e}^{y} y^{\prime }+2 x = 2 x \,{\mathrm e}^{y}
\] |
[_separable] |
✓ |
1.700 |
|
|
\[
{}y \,{\mathrm e}^{2 x} y^{\prime }+2 x = 0
\] |
[_separable] |
✓ |
3.712 |
|
|
\[
{}x y y^{\prime } = \sqrt {y^{2}-9}
\] |
[_separable] |
✓ |
3.695 |
|
|
\[
{}\left (x +y-1\right ) y^{\prime } = x -y+1
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.148 |
|
|
\[
{}x y y^{\prime } = 2 x^{2}-y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
62.476 |
|
|
\[
{}x^{2}-y^{2}+x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.033 |
|
|
\[
{}x^{2} y^{\prime }-2 x y-2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.891 |
|
|
\[
{}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
11.056 |
|
|
\[
{}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.742 |
|
|
\[
{}x y^{\prime } = y+2 \,{\mathrm e}^{-\frac {y}{x}}
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
1.949 |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.540 |
|
|
\[
{}y^{\prime } = \sin \left (x -y+1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
6.210 |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x -y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
36.808 |
|
|
\[
{}y^{\prime } = \frac {x +y+4}{x +y-6}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.814 |
|
|
\[
{}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.673 |
|
|
\[
{}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
40.543 |
|
|
\[
{}y-x^{3}+\left (x +y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.289 |
|
|
\[
{}2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime }
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.609 |
|
|
\[
{}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.252 |
|
|
\[
{}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.536 |
|
|
\[
{}\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right )
\] |
[_exact] |
✓ |
29.115 |
|
|
\[
{}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0
\] |
[_separable] |
✓ |
1.736 |
|
|
\[
{}1+y+\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.777 |
|
|
\[
{}2 x y^{3}+y \cos \left (x \right )+\left (3 y^{2} x^{2}+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
39.178 |
|
|
\[
{}1 = \frac {y}{1-y^{2} x^{2}}+\frac {x y^{\prime }}{1-y^{2} x^{2}}
\] |
[_exact, _rational, _Riccati] |
✓ |
1.671 |
|
|
\[
{}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
34.222 |
|
|
\[
{}x y-1+\left (x^{2}-x y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.288 |
|
|
\[
{}\left (x +3 x^{3} y^{4}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
11.630 |
|
|
\[
{}\left (x -1-y^{2}\right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.788 |
|
|
\[
{}y-\left (x +x y^{3}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.314 |
|
|
\[
{}x y^{\prime } = x^{5}+x^{3} y^{2}+y
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.938 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y-x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
39.176 |
|
|
\[
{}x y^{\prime } = y+x^{2}+9 y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.502 |
|
|
\[
{}x y^{\prime }-3 y = x^{4}
\] |
[_linear] |
✓ |
1.819 |
|
|
\[
{}y^{\prime }+y = \frac {1}{{\mathrm e}^{2 x}+1}
\] |
[_linear] |
✓ |
1.800 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = \cot \left (x \right )
\] |
[_linear] |
✓ |
1.805 |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.895 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 x \csc \left (x \right )
\] |
[_linear] |
✓ |
1.908 |
|
|
\[
{}2 y-x^{3} = x y^{\prime }
\] |
[_linear] |
✓ |
1.733 |
|
|
\[
{}\left (1-x y\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.651 |
|
|
\[
{}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
36.956 |
|
|
\[
{}x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
9.378 |
|
|
\[
{}y^{2} = \left (x^{3}-x y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.683 |
|
|
\[
{}x^{2} y^{3}+y = \left (x^{3} y^{2}-x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.994 |
|
|
\[
{}x y^{\prime }+y = x \cos \left (x \right )
\] |
[_linear] |
✓ |
1.417 |
|
|
\[
{}\left (x y-x^{2}\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
40.695 |
|
|
\[
{}\left ({\mathrm e}^{x}-3 y^{2} x^{2}\right ) y^{\prime }+y \,{\mathrm e}^{x} = 2 x y^{3}
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.067 |
|
|
\[
{}x^{2}+y = x y^{\prime }
\] |
[_linear] |
✓ |
1.661 |
|
|
\[
{}x y^{\prime }+y = x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.501 |
|
|
\[
{}6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.934 |
|
|
\[
{}\cos \left (x +y\right )-x \sin \left (x +y\right ) = x \sin \left (x +y\right ) y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
4.427 |
|
|
\[
{}y^{2} {\mathrm e}^{x y}+\cos \left (x \right )+\left ({\mathrm e}^{x y}+x y \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
35.586 |
|
|
\[
{}y^{\prime } \ln \left (x -y\right ) = 1+\ln \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
2.138 |
|
|
\[
{}y^{\prime }+2 x y = {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
1.695 |
|
|
\[
{}y^{2}-3 x y-2 x^{2} = \left (x^{2}-x y\right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
77.912 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y = 4 x^{3}
\] |
[_linear] |
✓ |
1.791 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )-y \sin \left (x y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )-x \sin \left (x y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
39.335 |
|
|
\[
{}\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime } = 2 x y-{\mathrm e}^{y}-x
\] |
[_exact] |
✓ |
1.931 |
|
|
\[
{}{\mathrm e}^{x} \left (x +1\right ) = \left (x \,{\mathrm e}^{x}-y \,{\mathrm e}^{y}\right ) y^{\prime }
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.870 |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.279 |
|
|
\[
{}x +y+\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.181 |
|
|
\[
{}\ln \left (x \right ) y^{\prime }+\frac {x +y}{x} = 0
\] |
[_linear] |
✓ |
1.329 |
|
|
\[
{}\cos \left (y\right )-x \sin \left (y\right ) y^{\prime } = \sec \left (x \right )^{2}
\] |
[_exact] |
✓ |
40.373 |
|
|
\[
{}y \sin \left (\frac {x}{y}\right )+x \cos \left (\frac {x}{y}\right )-1+\left (x \sin \left (\frac {x}{y}\right )-\frac {x^{2} \cos \left (\frac {x}{y}\right )}{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
37.272 |
|
|
\[
{}\frac {x}{x^{2}+y^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{x^{2}+y^{2}}-\frac {1}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
553.295 |
|