|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}1+y+\left (1-x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.180 |
|
|
\[
{}2 x y^{3}+y \cos \left (x \right )+\left (3 x^{2} y^{2}+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
82.871 |
|
|
\[
{}1 = \frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}}
\] |
[_exact, _rational, _Riccati] |
✓ |
2.919 |
|
|
\[
{}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 y x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
26.980 |
|
|
\[
{}y x -1+\left (x^{2}-y x \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.629 |
|
|
\[
{}\left (x +3 x^{3} y^{4}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
33.302 |
|
|
\[
{}\left (x -1-y^{2}\right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.838 |
|
|
\[
{}y-\left (x +x y^{3}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
12.589 |
|
|
\[
{}y^{\prime } x = x^{5}+x^{3} y^{2}+y
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
3.792 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = -x +y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
12.131 |
|
|
\[
{}y^{\prime } x = y+x^{2}+9 y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
9.241 |
|
|
\[
{}y^{\prime } x -3 y = x^{4}
\] |
[_linear] |
✓ |
2.855 |
|
|
\[
{}y^{\prime }+y = \frac {1}{{\mathrm e}^{2 x}+1}
\] |
[_linear] |
✓ |
2.802 |
|
|
\[
{}2 y x +\left (x^{2}+1\right ) y^{\prime } = \cot \left (x \right )
\] |
[_linear] |
✓ |
2.302 |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
9.241 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 x \csc \left (x \right )
\] |
[_linear] |
✓ |
3.305 |
|
|
\[
{}2 y-x^{3} = y^{\prime } x
\] |
[_linear] |
✓ |
8.297 |
|
|
\[
{}\left (1-y x \right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.381 |
|
|
\[
{}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
11.632 |
|
|
\[
{}y^{\prime } x = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
40.391 |
|
|
\[
{}y^{2} = \left (x^{3}-y x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
17.071 |
|
|
\[
{}x^{2} y^{3}+y = \left (x^{3} y^{2}-x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
11.023 |
|
|
\[
{}y^{\prime } x +y = x \cos \left (x \right )
\] |
[_linear] |
✓ |
2.378 |
|
|
\[
{}\left (y x -x^{2}\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
54.627 |
|
|
\[
{}\left ({\mathrm e}^{x}-3 x^{2} y^{2}\right ) y^{\prime }+y \,{\mathrm e}^{x} = 2 x y^{3}
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
4.823 |
|
|
\[
{}y+x^{2} = y^{\prime } x
\] |
[_linear] |
✓ |
8.240 |
|
|
\[
{}y^{\prime } x +y = x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
2.450 |
|
|
\[
{}6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.503 |
|
|
\[
{}\cos \left (x +y\right )-x \sin \left (x +y\right ) = x \sin \left (x +y\right ) y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
14.177 |
|
|
\[
{}y^{2} {\mathrm e}^{y x}+\cos \left (x \right )+\left ({\mathrm e}^{y x}+x y \,{\mathrm e}^{y x}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
69.405 |
|
|
\[
{}y^{\prime } \ln \left (x -y\right ) = 1+\ln \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
11.996 |
|
|
\[
{}y^{\prime }+2 y x = {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
2.014 |
|
|
\[
{}y^{2}-3 y x -2 x^{2} = \left (x^{2}-y x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
32.842 |
|
|
\[
{}2 y x +\left (x^{2}+1\right ) y^{\prime } = 4 x^{3}
\] |
[_linear] |
✓ |
8.128 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )-y \sin \left (y x \right )+\left ({\mathrm e}^{x} \cos \left (y\right )-x \sin \left (y x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
85.329 |
|
|
\[
{}\left (x \,{\mathrm e}^{y}+y-x^{2}\right ) y^{\prime } = 2 y x -{\mathrm e}^{y}-x
\] |
[_exact] |
✓ |
3.335 |
|
|
\[
{}{\mathrm e}^{x} \left (x +1\right ) = \left (x \,{\mathrm e}^{x}-y \,{\mathrm e}^{y}\right ) y^{\prime }
\] |
[‘y=_G(x,y’)‘] |
✓ |
8.688 |
|
|
\[
{}2 y x +x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
4.545 |
|
|
\[
{}x +y+\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
11.263 |
|
|
\[
{}\ln \left (x \right ) y^{\prime }+\frac {x +y}{x} = 0
\] |
[_linear] |
✓ |
2.378 |
|
|
\[
{}\cos \left (y\right )-x \sin \left (y\right ) y^{\prime } = \sec \left (x \right )^{2}
\] |
[_exact] |
✓ |
73.284 |
|
|
\[
{}y \sin \left (\frac {x}{y}\right )+x \cos \left (\frac {x}{y}\right )-1+\left (x \sin \left (\frac {x}{y}\right )-\frac {x^{2} \cos \left (\frac {x}{y}\right )}{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
85.066 |
|
|
\[
{}\frac {x}{x^{2}+y^{2}}+\frac {y}{x^{2}}+\left (\frac {y}{x^{2}+y^{2}}-\frac {1}{x}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
335.118 |
|
|
\[
{}x^{2} \left (1+y^{2}\right ) y^{\prime }+y^{2} \left (x^{2}+1\right ) = 0
\] |
[_separable] |
✓ |
9.882 |
|
|
\[
{}x \left (x -1\right ) y^{\prime } = \cot \left (y\right )
\] |
[_separable] |
✓ |
7.606 |
|
|
\[
{}r y^{\prime } = \frac {\left (a^{2}-r^{2}\right ) \tan \left (y\right )}{a^{2}+r^{2}}
\] |
[_separable] |
✓ |
12.216 |
|
|
\[
{}\sqrt {x^{2}+1}\, y^{\prime }+\sqrt {1+y^{2}} = 0
\] |
[_separable] |
✓ |
18.173 |
|
|
\[
{}y^{\prime } = \frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )}
\] |
[_separable] |
✓ |
15.033 |
|
|
\[
{}y^{2} y^{\prime } = 2+3 y^{6}
\] |
[_quadrature] |
✓ |
5.126 |
|
|
\[
{}\cos \left (y\right )^{2}+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
12.266 |
|
|
\[
{}y^{\prime } = \frac {x^{3} {\mathrm e}^{x^{2}}}{y \ln \left (y\right )}
\] |
[_separable] |
✓ |
8.947 |
|
|
\[
{}x \cos \left (y\right )^{2}+{\mathrm e}^{x} \tan \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
33.195 |
|
|
\[
{}x \left (1+y^{2}\right )+\left (2 y+1\right ) {\mathrm e}^{-x} y^{\prime } = 0
\] |
[_separable] |
✓ |
4.329 |
|
|
\[
{}x y^{3}+{\mathrm e}^{x^{2}} y^{\prime } = 0
\] |
[_separable] |
✓ |
4.574 |
|
|
\[
{}x \cos \left (y\right )^{2}+\tan \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
95.652 |
|
|
\[
{}x y^{3}+\left (1+y\right ) {\mathrm e}^{-x} y^{\prime } = 0
\] |
[_separable] |
✓ |
11.782 |
|
|
\[
{}y^{\prime }+\frac {x}{y}+2 = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.606 |
|
|
\[
{}y^{\prime } x -y = x \cot \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
46.014 |
|
|
\[
{}x \cos \left (\frac {y}{x}\right )^{2}-y+y^{\prime } x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
18.961 |
|
|
\[
{}y^{\prime } x = y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
30.804 |
|
|
\[
{}y x +\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
49.836 |
|
|
\[
{}\left (1-{\mathrm e}^{-\frac {y}{x}}\right ) y^{\prime }+1-\frac {y}{x} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
27.725 |
|
|
\[
{}x^{2}-y x +y^{2}-x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
34.896 |
|
|
\[
{}\left (3+2 x +4 y\right ) y^{\prime } = 1+x +2 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.204 |
|
|
\[
{}y^{\prime } = \frac {2 x +y-1}{x -y-2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
29.322 |
|
|
\[
{}y+2 = \left (2 x +y-4\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
18.258 |
|
|
\[
{}y^{\prime } = \sin \left (x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
22.175 |
|
|
\[
{}y^{\prime } = \left (x +1\right )^{2}+\left (4 y+1\right )^{2}+8 y x +1
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
57.603 |
|
|
\[
{}3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
3.983 |
|
|
\[
{}2 x^{2}-x y^{2}-2 y+3-\left (x^{2} y+2 x \right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
9.832 |
|
|
\[
{}x y^{2}+x -2 y+3+\left (x^{2} y-2 x -2 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.121 |
|
|
\[
{}3 y \left (x^{2}-1\right )+\left (x^{3}+8 y-3 x \right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.747 |
|
|
\[
{}x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y} = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
12.447 |
|
|
\[
{}2 x \left (3 x +y-y \,{\mathrm e}^{-x^{2}}\right )+\left (x^{2}+3 y^{2}+{\mathrm e}^{-x^{2}}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
69.194 |
|
|
\[
{}3+y+2 y^{2} \sin \left (x \right )^{2}+\left (x +2 y x -y \sin \left (2 x \right )\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
77.520 |
|
|
\[
{}2 y x +\left (x^{2}+2 y x +y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
121.515 |
|
|
\[
{}x^{2}-\sin \left (y\right )^{2}+x \sin \left (2 y\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
12.660 |
|
|
\[
{}y \left (2 x -y+2\right )+2 \left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.441 |
|
|
\[
{}4 y x +3 y^{2}-x +x \left (x +2 y\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.066 |
|
|
\[
{}y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
14.836 |
|
|
\[
{}x^{2}+2 x +y+\left (3 x^{2} y-x \right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
9.017 |
|
|
\[
{}y^{2}+\left (y x +y^{2}-1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
2.352 |
|
|
\[
{}3 x^{2}+3 y^{2}+x \left (x^{2}+3 y^{2}+6 y\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
2.425 |
|
|
\[
{}2 y \left (x +y+2\right )+\left (y^{2}-x^{2}-4 x -1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
15.153 |
|
|
\[
{}2+y^{2}+2 x +2 y y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
3.322 |
|
|
\[
{}2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
2.631 |
|
|
\[
{}y \left (x +y\right )+\left (x +2 y-1\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.418 |
|
|
\[
{}2 x \left (x^{2}-\sin \left (y\right )+1\right )+\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
5.659 |
|
|
\[
{}x^{2}+y+y^{2}-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
11.357 |
|
|
\[
{}x -\sqrt {x^{2}+y^{2}}+\left (y-\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
113.238 |
|
|
\[
{}y \sqrt {1+y^{2}}+\left (x \sqrt {1+y^{2}}-y\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
16.023 |
|
|
\[
{}y^{2}-\left (y x +x^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
19.836 |
|
|
\[
{}y-2 x^{3} \tan \left (\frac {y}{x}\right )-y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘]] |
✓ |
11.952 |
|
|
\[
{}2 x^{2} y^{2}+y+\left (x^{3} y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.131 |
|
|
\[
{}y^{2}+\left (y x +\tan \left (y x \right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
71.860 |
|
|
\[
{}2 x^{2} y^{4}-y+\left (4 x^{3} y^{3}-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
23.493 |
|
|
\[
{}x^{2}+y^{3}+y+\left (x^{3}+y^{2}-x \right ) y^{\prime } = 0
\] |
[_rational] |
✗ |
2.790 |
|
|
\[
{}y \left (1+y^{2}\right )+x \left (y^{2}-x +1\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
4.233 |
|
|
\[
{}y^{2}+\left ({\mathrm e}^{x}-y\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
9.437 |
|
|
\[
{}x^{2} y^{2}-2 y+\left (x^{3} y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.660 |
|