|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 2 x y^{2}+3 x^{2} y^{2}
\] |
[_separable] |
✓ |
3.825 |
|
|
\[
{}y^{\prime } = 6 \,{\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
5.162 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime } = \cos \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.800 |
|
|
\[
{}y^{\prime }+y = 2
\] |
[_quadrature] |
✓ |
0.447 |
|
|
\[
{}-2 y+y^{\prime } = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.412 |
|
|
\[
{}3 y+y^{\prime } = 2 x \,{\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.769 |
|
|
\[
{}-2 y x +y^{\prime } = {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
2.536 |
|
|
\[
{}2 y+y^{\prime } x = 3 x
\] |
[_linear] |
✓ |
4.155 |
|
|
\[
{}2 y^{\prime } x +y = 10 \sqrt {x}
\] |
[_linear] |
✓ |
8.132 |
|
|
\[
{}2 y^{\prime } x +y = 10 \sqrt {x}
\] |
[_linear] |
✓ |
1.837 |
|
|
\[
{}y+3 y^{\prime } x = 12 x
\] |
[_linear] |
✓ |
3.830 |
|
|
\[
{}y^{\prime } x -y = x
\] |
[_linear] |
✓ |
3.819 |
|
|
\[
{}-3 y+2 y^{\prime } x = 9 x^{3}
\] |
[_linear] |
✓ |
1.871 |
|
|
\[
{}y^{\prime } x +y = 3 y x
\] |
[_separable] |
✓ |
2.777 |
|
|
\[
{}3 y+y^{\prime } x = 2 x^{5}
\] |
[_linear] |
✓ |
3.827 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.697 |
|
|
\[
{}-3 y+y^{\prime } x = x^{3}
\] |
[_linear] |
✓ |
2.486 |
|
|
\[
{}2 y x +y^{\prime } = x
\] |
[_separable] |
✓ |
2.747 |
|
|
\[
{}y^{\prime } = \cos \left (x \right ) \left (1-y\right )
\] |
[_separable] |
✓ |
3.072 |
|
|
\[
{}y+\left (x +1\right ) y^{\prime } = \cos \left (x \right )
\] |
[_linear] |
✓ |
2.257 |
|
|
\[
{}y^{\prime } x = x^{3} \cos \left (x \right )+2 y
\] |
[_linear] |
✓ |
1.463 |
|
|
\[
{}\cot \left (x \right ) y+y^{\prime } = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.605 |
|
|
\[
{}y^{\prime } = 1+x +y+y x
\] |
[_separable] |
✓ |
1.921 |
|
|
\[
{}y^{\prime } x = x^{4} \cos \left (x \right )+3 y
\] |
[_linear] |
✓ |
2.998 |
|
|
\[
{}y^{\prime } = 3 \,{\mathrm e}^{x^{2}} x^{2}+2 y x
\] |
[_linear] |
✓ |
2.956 |
|
|
\[
{}\left (2 x -3\right ) y+y^{\prime } x = 4 x^{4}
\] |
[_linear] |
✓ |
2.704 |
|
|
\[
{}3 y x +\left (x^{2}+4\right ) y^{\prime } = x
\] |
[_separable] |
✓ |
1.252 |
|
|
\[
{}3 x^{3} y+\left (x^{2}+1\right ) y^{\prime } = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}}
\] |
[_linear] |
✓ |
2.561 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = x -y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.122 |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
11.712 |
|
|
\[
{}y^{\prime } x = y+2 \sqrt {y x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.044 |
|
|
\[
{}\left (x -y\right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.461 |
|
|
\[
{}x \left (x +y\right ) y^{\prime } = y \left (x -y\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.360 |
|
|
\[
{}\left (x +2 y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.020 |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
14.178 |
|
|
\[
{}x^{2} y^{\prime } = {\mathrm e}^{\frac {y}{x}} x^{2}+y x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
20.486 |
|
|
\[
{}x^{2} y^{\prime } = y x +y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.617 |
|
|
\[
{}x y y^{\prime } = x^{2}+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
8.016 |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 y x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.574 |
|
|
\[
{}x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
40.931 |
|
|
\[
{}y^{\prime } x = y+\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
11.014 |
|
|
\[
{}x +y y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
11.293 |
|
|
\[
{}y \left (3 x +y\right )+x \left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
10.523 |
|
|
\[
{}y^{\prime } = \sqrt {x +y+1}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
4.535 |
|
|
\[
{}y^{\prime } = \left (4 x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.188 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.204 |
|
|
\[
{}2 y x +x^{2} y^{\prime } = 5 y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
4.921 |
|
|
\[
{}2 x y^{3}+y^{2} y^{\prime } = 6 x
\] |
[_separable] |
✓ |
3.206 |
|
|
\[
{}y^{\prime } = y+y^{3}
\] |
[_quadrature] |
✓ |
4.507 |
|
|
\[
{}2 y x +x^{2} y^{\prime } = 5 y^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
5.086 |
|
|
\[
{}y^{\prime } x +6 y = 3 x y^{{4}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
92.378 |
|
|
\[
{}y^{3} {\mathrm e}^{-2 x}+2 y^{\prime } x = 2 y x
\] |
[_Bernoulli] |
✓ |
3.992 |
|
|
\[
{}y^{2} \left (y^{\prime } x +y\right ) \sqrt {x^{4}+1} = x
\] |
[_Bernoulli] |
✓ |
13.171 |
|
|
\[
{}y^{3}+3 y^{2} y^{\prime } = {\mathrm e}^{-x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.770 |
|
|
\[
{}3 x y^{2} y^{\prime } = 3 x^{4}+y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
4.873 |
|
|
\[
{}{\mathrm e}^{y} x y^{\prime } = 2 \,{\mathrm e}^{y}+2 x^{3} {\mathrm e}^{2 x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.758 |
|
|
\[
{}2 x \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 4 x^{2}+\sin \left (y\right )^{2}
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.408 |
|
|
\[
{}\left ({\mathrm e}^{y}+x \right ) y^{\prime } = -1+x \,{\mathrm e}^{-y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.768 |
|
|
\[
{}2 x +3 y+\left (3 x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.878 |
|
|
\[
{}4 x -y+\left (-x +6 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.169 |
|
|
\[
{}3 x^{2}+2 y^{2}+\left (4 y x +6 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
13.801 |
|
|
\[
{}3 x^{2}+2 x y^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.804 |
|
|
\[
{}x^{3}+\frac {y}{x}+\left (y^{2}+\ln \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.763 |
|
|
\[
{}1+y \,{\mathrm e}^{y x}+\left (2 y+x \,{\mathrm e}^{y x}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.305 |
|
|
\[
{}\cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
6.551 |
|
|
\[
{}x +\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}} = 0
\] |
[_exact] |
✓ |
1.581 |
|
|
\[
{}3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+4 x y^{3}+y^{4}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
2.715 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
26.570 |
|
|
\[
{}\frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}+\frac {2 y}{x^{3}}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
18.954 |
|
|
\[
{}\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
3.746 |
|
|
\[
{}x^{3}+3 y-y^{\prime } x = 0
\] |
[_linear] |
✓ |
0.844 |
|
|
\[
{}3 y^{2}+x y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.405 |
|
|
\[
{}y x +y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.204 |
|
|
\[
{}{\mathrm e}^{x}+2 x y^{3}+\left (3 x^{2} y^{2}+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.207 |
|
|
\[
{}3 y+x^{4} y^{\prime } = 2 y x
\] |
[_separable] |
✓ |
2.583 |
|
|
\[
{}2 x y^{2}+x^{2} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
1.477 |
|
|
\[
{}2 x^{2} y+x^{3} y^{\prime } = 1
\] |
[_linear] |
✓ |
0.895 |
|
|
\[
{}2 y x +x^{2} y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
6.133 |
|
|
\[
{}2 y+y^{\prime } x = 6 x^{2} \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
6.468 |
|
|
\[
{}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{2}
\] |
[_separable] |
✓ |
2.961 |
|
|
\[
{}x^{2} y^{\prime } = y x +3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.952 |
|
|
\[
{}6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
12.522 |
|
|
\[
{}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{4}
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.591 |
|
|
\[
{}x^{3} y^{\prime } = x^{2} y-y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
79.856 |
|
|
\[
{}3 y+y^{\prime } = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.866 |
|
|
\[
{}y^{\prime } = x^{2}-2 y x +y^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.523 |
|
|
\[
{}{\mathrm e}^{x}+y \,{\mathrm e}^{y x}+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{y x}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
4.718 |
|
|
\[
{}2 x^{2} y-x^{3} y^{\prime } = y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
95.566 |
|
|
\[
{}3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2}
\] |
[_separable] |
✓ |
1.529 |
|
|
\[
{}3 y+y^{\prime } x = \frac {3}{x^{{3}/{2}}}
\] |
[_linear] |
✓ |
3.576 |
|
|
\[
{}\left (x -1\right ) y+\left (x^{2}-1\right ) y^{\prime } = 1
\] |
[_linear] |
✓ |
1.104 |
|
|
\[
{}y^{\prime } x = 12 x^{4} y^{{2}/{3}}+6 y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
10.925 |
|
|
\[
{}{\mathrm e}^{y}+y \cos \left (x \right )+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
72.859 |
|
|
\[
{}9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
3.546 |
|
|
\[
{}2 y+\left (x +1\right ) y^{\prime } = 3+3 x
\] |
[_linear] |
✓ |
1.519 |
|
|
\[
{}9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
0.209 |
|
|
\[
{}3 y+x^{3} y^{4}+3 y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
4.113 |
|
|
\[
{}y^{\prime } x +y = 2 \,{\mathrm e}^{2 x}
\] |
[_linear] |
✓ |
0.996 |
|
|
\[
{}y+\left (2 x +1\right ) y^{\prime } = \left (2 x +1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
6.008 |
|
|
\[
{}y^{\prime } = 3 x^{2} \left (7+y\right )
\] |
[_separable] |
✓ |
0.981 |
|