|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } x +\left (5 x +2\right ) y = \frac {20}{x}
\] |
[_linear] |
✓ |
2.276 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime }+y = 2 x \,{\mathrm e}^{-\sqrt {x}}
\] |
[_linear] |
✓ |
2.717 |
|
|
\[
{}y^{\prime }-3 y = 6
\] |
[_quadrature] |
✓ |
1.491 |
|
|
\[
{}y^{\prime }-3 y = 6
\] |
[_quadrature] |
✓ |
1.125 |
|
|
\[
{}y^{\prime }+5 y = {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.566 |
|
|
\[
{}y^{\prime } x +3 y = 20 x^{2}
\] |
[_linear] |
✓ |
2.142 |
|
|
\[
{}y^{\prime } x = y+x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.840 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (3+3 x^{2}-y\right )
\] |
[_linear] |
✓ |
4.289 |
|
|
\[
{}y^{\prime }+6 x y = \sin \left (x \right )
\] |
[_linear] |
✓ |
1.730 |
|
|
\[
{}x^{2} y^{\prime }+x y = \sqrt {x}\, \sin \left (x \right )
\] |
[_linear] |
✓ |
2.096 |
|
|
\[
{}-y+y^{\prime } x = x^{2} {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
1.858 |
|
|
\[
{}y^{\prime } = \frac {1}{\left (3 x +3 y+2\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
5.625 |
|
|
\[
{}y^{\prime } = \frac {\left (3 x -2 y\right )^{2}+1}{3 x -2 y}+\frac {3}{2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.955 |
|
|
\[
{}\cos \left (-4 y+8 x -3\right ) y^{\prime } = 2+2 \cos \left (-4 y+8 x -3\right )
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
115.649 |
|
|
\[
{}y^{\prime } = 1+\left (y-x \right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
2.959 |
|
|
\[
{}x^{2} y^{\prime }-x y = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.329 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\frac {x}{y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.802 |
|
|
\[
{}\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right ) = 1+\sin \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.668 |
|
|
\[
{}y^{\prime } = \frac {x -y}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.981 |
|
|
\[
{}y^{\prime }+3 y = 3 y^{3}
\] |
[_quadrature] |
✓ |
3.487 |
|
|
\[
{}y^{\prime }-\frac {3 y}{x} = \frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.264 |
|
|
\[
{}y^{\prime }+3 \cot \left (x \right ) y = 6 \cos \left (x \right ) y^{{2}/{3}}
\] |
[_Bernoulli] |
✓ |
3.468 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = \frac {1}{y}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.999 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\frac {x^{2}}{y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.623 |
|
|
\[
{}3 y^{\prime } = -2+\sqrt {2 x +3 y+4}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.195 |
|
|
\[
{}3 y^{\prime }+\frac {2 y}{x} = 4 \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.626 |
|
|
\[
{}y^{\prime } = 4+\frac {1}{\sin \left (4 x -y\right )}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
38.771 |
|
|
\[
{}\left (y-x \right ) y^{\prime } = 1
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.523 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.811 |
|
|
\[
{}\left (2 x y+2 x^{2}\right ) y^{\prime } = x^{2}+2 x y+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
62.122 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x^{2} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.839 |
|
|
\[
{}y^{\prime } = 2 \sqrt {2 x +y-3}-2
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.358 |
|
|
\[
{}y^{\prime } = 2 \sqrt {2 x +y-3}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.770 |
|
|
\[
{}-y+y^{\prime } x = \sqrt {x y+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.109 |
|
|
\[
{}y^{\prime }+3 y = \frac {28 \,{\mathrm e}^{2 x}}{y^{3}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
2.889 |
|
|
\[
{}y^{\prime } = \left (x -y+3\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
3.299 |
|
|
\[
{}y^{\prime }+2 x = 2 \sqrt {y+x^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.240 |
|
|
\[
{}\cos \left (y\right ) y^{\prime } = {\mathrm e}^{-x}-\sin \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.074 |
|
|
\[
{}y^{\prime } = x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right )
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.656 |
|
|
\[
{}y^{\prime } = \frac {1}{y}-\frac {y}{2 x}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.100 |
|
|
\[
{}{\mathrm e}^{x y^{2}-x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{x y^{2}-x^{2}} x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.108 |
|
|
\[
{}2 x y+y^{2}+\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.565 |
|
|
\[
{}2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.646 |
|
|
\[
{}2-2 x +3 y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.884 |
|
|
\[
{}1+3 x^{2} y^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
1.667 |
|
|
\[
{}4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
72.728 |
|
|
\[
{}1+\ln \left (x y\right )+\frac {x y^{\prime }}{y} = 0
\] |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
2.001 |
|
|
\[
{}1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.669 |
|
|
\[
{}{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries], _exact] |
✓ |
1.250 |
|
|
\[
{}1+y^{4}+x y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.237 |
|
|
\[
{}y+\left (y^{4}-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
8.214 |
|
|
\[
{}\frac {2 y}{x}+\left (4 x^{2} y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.511 |
|
|
\[
{}1+\left (1-x \tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.322 |
|
|
\[
{}3 y+3 y^{2}+\left (2 x +4 x y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.957 |
|
|
\[
{}2 x \left (1+y\right )-y^{\prime } = 0
\] |
[_separable] |
✓ |
1.418 |
|
|
\[
{}2 y^{3}+\left (4 x^{3} y^{3}-3 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.826 |
|
|
\[
{}4 x y+\left (3 x^{2}+5 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.823 |
|
|
\[
{}6+12 x^{2} y^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.461 |
|
|
\[
{}y^{\prime } x = 2 y-6 x^{3}
\] |
[_linear] |
✓ |
1.563 |
|
|
\[
{}y^{\prime } x = 2 y^{2}-6 y
\] |
[_separable] |
✓ |
2.333 |
|
|
\[
{}4 y^{2}-x^{2} y^{2}+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.696 |
|
|
\[
{}y^{\prime } = \sqrt {x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.141 |
|
|
\[
{}x^{2} y^{\prime }-\sqrt {x} = 3
\] |
[_quadrature] |
✓ |
0.457 |
|
|
\[
{}x y y^{\prime }-y^{2} = \sqrt {x^{4}+x^{2} y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
34.892 |
|
|
\[
{}y^{\prime } = y^{2}-2 x y+x^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.808 |
|
|
\[
{}4 x y-6+x^{2} y^{\prime } = 0
\] |
[_linear] |
✓ |
1.635 |
|
|
\[
{}x y^{2}-6+x^{2} y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.075 |
|
|
\[
{}x^{3}+y^{3}+x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
13.271 |
|
|
\[
{}3 y-x^{3}+y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.635 |
|
|
\[
{}1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
1.618 |
|
|
\[
{}3 x y^{3}-y+y^{\prime } x = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.738 |
|
|
\[
{}2+2 x^{2}-2 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.658 |
|
|
\[
{}\left (y^{2}-4\right ) y^{\prime } = y
\] |
[_quadrature] |
✓ |
1.758 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.564 |
|
|
\[
{}y^{\prime } = \frac {1}{x y-3 x}
\] |
[_separable] |
✓ |
1.688 |
|
|
\[
{}y^{\prime } = \frac {3 y}{x +1}-y^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
1.526 |
|
|
\[
{}\sin \left (y\right )+\left (x +y\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.555 |
|
|
\[
{}\sin \left (y\right )+\left (x +1\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.615 |
|
|
\[
{}\sin \left (x \right )+2 y^{\prime } \cos \left (x \right ) = 0
\] |
[_quadrature] |
✓ |
0.638 |
|
|
\[
{}x y y^{\prime } = 2 x^{2}+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
10.120 |
|
|
\[
{}y^{\prime } = \frac {2 y+x}{x +2 y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.804 |
|
|
\[
{}y^{\prime } = \frac {2 y+x}{2 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.569 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.416 |
|
|
\[
{}y^{\prime } = x y^{2}+3 y^{2}+x +3
\] |
[_separable] |
✓ |
2.340 |
|
|
\[
{}1-\left (2 y+x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.728 |
|
|
\[
{}\ln \left (y\right )+\left (\frac {x}{y}+3\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.139 |
|
|
\[
{}y^{2}+1-y^{\prime } = 0
\] |
[_quadrature] |
✓ |
1.191 |
|
|
\[
{}y^{\prime }-3 y = 12 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.365 |
|
|
\[
{}x y y^{\prime } = x^{2}+x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
37.254 |
|
|
\[
{}\left (x +2\right ) y^{\prime }-x^{3} = 0
\] |
[_quadrature] |
✓ |
0.551 |
|
|
\[
{}x y^{3} y^{\prime } = y^{4}-x^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.741 |
|
|
\[
{}y^{\prime } = 4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
2.165 |
|
|
\[
{}2 y-6 x +\left (x +1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.760 |
|
|
\[
{}x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
2.097 |
|
|
\[
{}y y^{\prime }-x y^{2} = 6 x \,{\mathrm e}^{4 x^{2}}
\] |
[_Bernoulli] |
✓ |
2.333 |
|
|
\[
{}\left (y-x +3\right )^{2} \left (y^{\prime }-1\right ) = 1
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, _dAlembert] |
✓ |
9.692 |
|
|
\[
{}x +y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.382 |
|
|
\[
{}y^{2}-y^{2} \cos \left (x \right )+y^{\prime } = 0
\] |
[_separable] |
✓ |
2.044 |
|
|
\[
{}y^{\prime }+2 y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.337 |
|
|
\[
{}y^{\prime }+2 x = \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.536 |
|