|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{\prime } = y^{2}-y
\] |
[_separable] |
✓ |
2.737 |
|
|
\[
{}y^{\prime } = \frac {y^{2}-1}{x y}
\] |
[_separable] |
✓ |
4.978 |
|
|
\[
{}\left (y^{2}-1\right ) y^{\prime } = 4 x y
\] |
[_separable] |
✓ |
2.192 |
|
|
\[
{}x^{2} y^{\prime }+3 x^{2} y = \sin \left (x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.033 |
|
|
\[
{}y^{2} y^{\prime }+3 x^{2} y = \sin \left (x \right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.688 |
|
|
\[
{}y^{\prime }-x y^{2} = \sqrt {x}
\] |
[_Riccati] |
✓ |
1.788 |
|
|
\[
{}y^{\prime } = 1+\left (x y+3 y\right )^{2}
\] |
[_Riccati] |
✓ |
2.551 |
|
|
\[
{}y^{\prime } = 1+x y+3 y
\] |
[_linear] |
✓ |
1.431 |
|
|
\[
{}y^{\prime } = 4 y+8
\] |
[_quadrature] |
✓ |
1.520 |
|
|
\[
{}y^{\prime }-{\mathrm e}^{2 x} = 0
\] |
[_quadrature] |
✓ |
0.485 |
|
|
\[
{}y^{\prime } = y \sin \left (x \right )
\] |
[_separable] |
✓ |
2.023 |
|
|
\[
{}y^{\prime }+4 y = y^{3}
\] |
[_quadrature] |
✓ |
4.231 |
|
|
\[
{}x y^{\prime }+\cos \left (x^{2}\right ) = 827 y
\] |
[_linear] |
✓ |
23.692 |
|
|
\[
{}y^{\prime }+2 y = 6
\] |
[_quadrature] |
✓ |
1.684 |
|
|
\[
{}y^{\prime }+2 y = 20 \,{\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.446 |
|
|
\[
{}y^{\prime } = 4 y+16 x
\] |
[[_linear, ‘class A‘]] |
✓ |
1.302 |
|
|
\[
{}y^{\prime }-2 x y = x
\] |
[_separable] |
✓ |
1.576 |
|
|
\[
{}x y^{\prime }+3 y-10 x^{2} = 0
\] |
[_linear] |
✓ |
1.716 |
|
|
\[
{}x^{2} y^{\prime }+2 x y = \sin \left (x \right )
\] |
[_linear] |
✓ |
1.563 |
|
|
\[
{}x y^{\prime } = \sqrt {x}+3 y
\] |
[_linear] |
✓ |
1.738 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y \sin \left (x \right ) = \cos \left (x \right )^{2}
\] |
[_linear] |
✓ |
2.717 |
|
|
\[
{}x y^{\prime }+\left (5 x +2\right ) y = \frac {20}{x}
\] |
[_linear] |
✓ |
2.505 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime }+y = 2 x \,{\mathrm e}^{-\sqrt {x}}
\] |
[_linear] |
✓ |
3.139 |
|
|
\[
{}y^{\prime }-3 y = 6
\] |
[_quadrature] |
✓ |
2.154 |
|
|
\[
{}y^{\prime }-3 y = 6
\] |
[_quadrature] |
✓ |
1.449 |
|
|
\[
{}y^{\prime }+5 y = {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.701 |
|
|
\[
{}x y^{\prime }+3 y = 20 x^{2}
\] |
[_linear] |
✓ |
2.207 |
|
|
\[
{}x y^{\prime } = y+x^{2} \cos \left (x \right )
\] |
[_linear] |
✓ |
2.099 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (3+3 x^{2}-y\right )
\] |
[_linear] |
✓ |
4.866 |
|
|
\[
{}y^{\prime }+6 x y = \sin \left (x \right )
\] |
[_linear] |
✓ |
2.083 |
|
|
\[
{}x^{2} y^{\prime }+x y = \sqrt {x}\, \sin \left (x \right )
\] |
[_linear] |
✓ |
2.345 |
|
|
\[
{}-y+x y^{\prime } = x^{2} {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
2.041 |
|
|
\[
{}y^{\prime } = \frac {1}{\left (3 x +3 y+2\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
6.950 |
|
|
\[
{}y^{\prime } = \frac {\left (-2 y+3 x \right )^{2}+1}{-2 y+3 x}+\frac {3}{2}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
11.439 |
|
|
\[
{}\cos \left (-4 y+8 x -3\right ) y^{\prime } = 2+2 \cos \left (-4 y+8 x -3\right )
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
142.836 |
|
|
\[
{}y^{\prime } = 1+\left (y-x \right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
2.363 |
|
|
\[
{}x^{2} y^{\prime }-x y = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.545 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\frac {x}{y}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.341 |
|
|
\[
{}\cos \left (\frac {y}{x}\right ) \left (y^{\prime }-\frac {y}{x}\right ) = 1+\sin \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.475 |
|
|
\[
{}y^{\prime } = \frac {x -y}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
12.411 |
|
|
\[
{}y^{\prime }+3 y = 3 y^{3}
\] |
[_quadrature] |
✓ |
4.251 |
|
|
\[
{}y^{\prime }-\frac {3 y}{x} = \frac {y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.562 |
|
|
\[
{}y^{\prime }+3 \cot \left (x \right ) y = 6 \cos \left (x \right ) y^{{2}/{3}}
\] |
[_Bernoulli] |
✓ |
4.024 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = \frac {1}{y}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.877 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\frac {x^{2}}{y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
11.821 |
|
|
\[
{}3 y^{\prime } = -2+\sqrt {2 x +3 y+4}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.465 |
|
|
\[
{}3 y^{\prime }+\frac {2 y}{x} = 4 \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
5.741 |
|
|
\[
{}y^{\prime } = 4+\frac {1}{\sin \left (4 x -y\right )}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
39.075 |
|
|
\[
{}\left (y-x \right ) y^{\prime } = 1
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.585 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.330 |
|
|
\[
{}\left (2 x y+2 x^{2}\right ) y^{\prime } = x^{2}+2 x y+2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
19.948 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = x^{2} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.612 |
|
|
\[
{}y^{\prime } = 2 \sqrt {2 x +y-3}-2
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.520 |
|
|
\[
{}y^{\prime } = 2 \sqrt {2 x +y-3}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.161 |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x y+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.427 |
|
|
\[
{}y^{\prime }+3 y = \frac {28 \,{\mathrm e}^{2 x}}{y^{3}}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
3.359 |
|
|
\[
{}y^{\prime } = \left (x -y+3\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
3.128 |
|
|
\[
{}y^{\prime }+2 x = 2 \sqrt {y+x^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.426 |
|
|
\[
{}\cos \left (y\right ) y^{\prime } = {\mathrm e}^{-x}-\sin \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.349 |
|
|
\[
{}y^{\prime } = x \left (1+\frac {2 y}{x^{2}}+\frac {y^{2}}{x^{4}}\right )
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.712 |
|
|
\[
{}y^{\prime } = \frac {1}{y}-\frac {y}{2 x}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.421 |
|
|
\[
{}{\mathrm e}^{x y^{2}-x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{x y^{2}-x^{2}} x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.463 |
|
|
\[
{}2 x y+y^{2}+\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
55.262 |
|
|
\[
{}2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.867 |
|
|
\[
{}2-2 x +3 y^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.209 |
|
|
\[
{}1+3 y^{2} x^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
2.346 |
|
|
\[
{}4 x^{3} y+\left (x^{4}-y^{4}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
71.034 |
|
|
\[
{}1+\ln \left (x y\right )+\frac {x y^{\prime }}{y} = 0
\] |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
2.495 |
|
|
\[
{}1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.838 |
|
|
\[
{}{\mathrm e}^{y}+\left (x \,{\mathrm e}^{y}+1\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries], _exact] |
✓ |
1.307 |
|
|
\[
{}1+y^{4}+x y^{3} y^{\prime } = 0
\] |
[_separable] |
✓ |
4.412 |
|
|
\[
{}y+\left (y^{4}-3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.956 |
|
|
\[
{}\frac {2 y}{x}+\left (4 x^{2} y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.961 |
|
|
\[
{}1+\left (1-x \tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.542 |
|
|
\[
{}3 y+3 y^{2}+\left (2 x +4 x y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
5.236 |
|
|
\[
{}2 x \left (y+1\right )-y^{\prime } = 0
\] |
[_separable] |
✓ |
1.514 |
|
|
\[
{}2 y^{3}+\left (4 x^{3} y^{3}-3 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.105 |
|
|
\[
{}4 x y+\left (3 x^{2}+5 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.032 |
|
|
\[
{}6+12 y^{2} x^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.029 |
|
|
\[
{}x y^{\prime } = 2 y-6 x^{3}
\] |
[_linear] |
✓ |
1.806 |
|
|
\[
{}x y^{\prime } = 2 y^{2}-6 y
\] |
[_separable] |
✓ |
2.637 |
|
|
\[
{}4 y^{2}-y^{2} x^{2}+y^{\prime } = 0
\] |
[_separable] |
✓ |
1.867 |
|
|
\[
{}y^{\prime } = \sqrt {x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.722 |
|
|
\[
{}x^{2} y^{\prime }-\sqrt {x} = 3
\] |
[_quadrature] |
✓ |
0.515 |
|
|
\[
{}x y y^{\prime }-y^{2} = \sqrt {x^{4}+y^{2} x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
12.694 |
|
|
\[
{}y^{\prime } = y^{2}-2 x y+x^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.992 |
|
|
\[
{}4 x y-6+x^{2} y^{\prime } = 0
\] |
[_linear] |
✓ |
1.908 |
|
|
\[
{}x y^{2}-6+x^{2} y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.421 |
|
|
\[
{}x^{3}+y^{3}+x y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
16.497 |
|
|
\[
{}3 y-x^{3}+x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.680 |
|
|
\[
{}1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
2.267 |
|
|
\[
{}3 x y^{3}-y+x y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.171 |
|
|
\[
{}2+2 x^{2}-2 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.788 |
|
|
\[
{}\left (y^{2}-4\right ) y^{\prime } = y
\] |
[_quadrature] |
✓ |
1.532 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.539 |
|
|
\[
{}y^{\prime } = \frac {1}{x y-3 x}
\] |
[_separable] |
✓ |
2.237 |
|
|
\[
{}y^{\prime } = \frac {3 y}{x +1}-y^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
1.908 |
|
|
\[
{}\sin \left (y\right )+\left (x +y\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
4.697 |
|
|
\[
{}\sin \left (y\right )+\left (x +1\right ) \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
4.809 |
|
|
\[
{}\sin \left (x \right )+2 \cos \left (x \right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.731 |
|