|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 2 x y^{2}+3 y^{2} x^{2}
\] |
[_separable] |
✓ |
2.225 |
|
|
\[
{}y^{\prime } = 6 \,{\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
4.343 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime } = \cos \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.010 |
|
|
\[
{}y+y^{\prime } = 2
\] |
[_quadrature] |
✓ |
1.848 |
|
|
\[
{}-2 y+y^{\prime } = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.619 |
|
|
\[
{}y^{\prime }+3 y = 2 x \,{\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.829 |
|
|
\[
{}y^{\prime }-2 x y = {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
1.684 |
|
|
\[
{}2 y+x y^{\prime } = 3 x
\] |
[_linear] |
✓ |
3.157 |
|
|
\[
{}y+2 x y^{\prime } = 10 \sqrt {x}
\] |
[_linear] |
✓ |
5.052 |
|
|
\[
{}y+2 x y^{\prime } = 10 \sqrt {x}
\] |
[_linear] |
✓ |
4.299 |
|
|
\[
{}y+3 x y^{\prime } = 12 x
\] |
[_linear] |
✓ |
2.407 |
|
|
\[
{}x y^{\prime }-y = x
\] |
[_linear] |
✓ |
1.959 |
|
|
\[
{}-3 y+2 x y^{\prime } = 9 x^{3}
\] |
[_linear] |
✓ |
1.630 |
|
|
\[
{}x y^{\prime }+y = 3 x y
\] |
[_separable] |
✓ |
2.481 |
|
|
\[
{}x y^{\prime }+3 y = 2 x^{5}
\] |
[_linear] |
✓ |
1.799 |
|
|
\[
{}y+y^{\prime } = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.551 |
|
|
\[
{}-3 y+x y^{\prime } = x^{3}
\] |
[_linear] |
✓ |
1.581 |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
1.964 |
|
|
\[
{}y^{\prime } = \cos \left (x \right ) \left (1-y\right )
\] |
[_separable] |
✓ |
2.241 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.957 |
|
|
\[
{}x y^{\prime } = x^{3} \cos \left (x \right )+2 y
\] |
[_linear] |
✓ |
1.846 |
|
|
\[
{}\cot \left (x \right ) y+y^{\prime } = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.938 |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
1.962 |
|
|
\[
{}x y^{\prime } = 3 y+x^{4} \cos \left (x \right )
\] |
[_linear] |
✓ |
2.860 |
|
|
\[
{}y^{\prime } = 3 x^{2} {\mathrm e}^{x^{2}}+2 x y
\] |
[_linear] |
✓ |
3.019 |
|
|
\[
{}\left (-3+2 x \right ) y+x y^{\prime } = 4 x^{4}
\] |
[_linear] |
✓ |
2.520 |
|
|
\[
{}3 x y+\left (x^{2}+4\right ) y^{\prime } = x
\] |
[_separable] |
✓ |
2.373 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}}
\] |
[_linear] |
✓ |
2.665 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = x -y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.268 |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.208 |
|
|
\[
{}x y^{\prime } = y+2 \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.945 |
|
|
\[
{}\left (x -y\right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
38.127 |
|
|
\[
{}x \left (x +y\right ) y^{\prime } = y \left (x -y\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
88.797 |
|
|
\[
{}\left (x +2 y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.168 |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
11.345 |
|
|
\[
{}x^{2} y^{\prime } = {\mathrm e}^{\frac {y}{x}} x^{2}+x y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
201.691 |
|
|
\[
{}x^{2} y^{\prime } = x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.401 |
|
|
\[
{}x y y^{\prime } = x^{2}+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
75.796 |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.737 |
|
|
\[
{}x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
113.476 |
|
|
\[
{}x y^{\prime } = y+\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.222 |
|
|
\[
{}x +y y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.916 |
|
|
\[
{}y \left (3 x +y\right )+x \left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
54.476 |
|
|
\[
{}y^{\prime } = \sqrt {1+x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.700 |
|
|
\[
{}y^{\prime } = \left (4 x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.586 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.575 |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 5 y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.211 |
|
|
\[
{}2 x y^{3}+y^{2} y^{\prime } = 6 x
\] |
[_separable] |
✓ |
2.472 |
|
|
\[
{}y^{\prime } = y+y^{3}
\] |
[_quadrature] |
✓ |
4.836 |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 5 y^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.062 |
|
|
\[
{}6 y+x y^{\prime } = 3 x y^{{4}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
97.482 |
|
|
\[
{}y^{3} {\mathrm e}^{-2 x}+2 x y^{\prime } = 2 x y
\] |
[_Bernoulli] |
✓ |
2.721 |
|
|
\[
{}\sqrt {x^{4}+1}\, y^{2} \left (x y^{\prime }+y\right ) = x
\] |
[_Bernoulli] |
✓ |
6.411 |
|
|
\[
{}y^{3}+3 y^{2} y^{\prime } = {\mathrm e}^{-x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
2.107 |
|
|
\[
{}3 x y^{2} y^{\prime } = 3 x^{4}+y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.684 |
|
|
\[
{}{\mathrm e}^{y} x y^{\prime } = 2 \,{\mathrm e}^{y}+2 x^{3} {\mathrm e}^{2 x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.737 |
|
|
\[
{}2 x \cos \left (y\right ) \sin \left (y\right ) y^{\prime } = 4 x^{2}+\sin \left (y\right )^{2}
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.274 |
|
|
\[
{}\left ({\mathrm e}^{y}+x \right ) y^{\prime } = -1+x \,{\mathrm e}^{-y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.939 |
|
|
\[
{}2 x +3 y+\left (3 x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.185 |
|
|
\[
{}4 x -y+\left (-x +6 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.930 |
|
|
\[
{}3 x^{2}+2 y^{2}+\left (4 x y+6 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
5.129 |
|
|
\[
{}3 x^{2}+2 x y^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
2.072 |
|
|
\[
{}x^{3}+\frac {y}{x}+\left (y^{2}+\ln \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.701 |
|
|
\[
{}1+y \,{\mathrm e}^{x y}+\left (2 y+x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.142 |
|
|
\[
{}\cos \left (x \right )+\ln \left (y\right )+\left ({\mathrm e}^{y}+\frac {x}{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
3.711 |
|
|
\[
{}x +\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}} = 0
\] |
[_exact] |
✓ |
1.965 |
|
|
\[
{}3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.664 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
17.374 |
|
|
\[
{}\frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}+\frac {2 y}{x^{3}}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
17.326 |
|
|
\[
{}\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (-2 x^{{5}/{2}}+3 y^{{5}/{3}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
2.405 |
|
|
\[
{}x^{3}+3 y-x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.294 |
|
|
\[
{}3 y^{2}+x y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.838 |
|
|
\[
{}x y+y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.397 |
|
|
\[
{}2 x y^{3}+{\mathrm e}^{x}+\left (3 y^{2} x^{2}+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.442 |
|
|
\[
{}3 y+x^{4} y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
1.989 |
|
|
\[
{}2 x y^{2}+x^{2} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
1.869 |
|
|
\[
{}2 x^{2} y+x^{3} y^{\prime } = 1
\] |
[_linear] |
✓ |
1.280 |
|
|
\[
{}2 x y+x^{2} y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.280 |
|
|
\[
{}2 y+x y^{\prime } = 6 x^{2} \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
5.329 |
|
|
\[
{}y^{\prime } = 1+x^{2}+y^{2}+y^{2} x^{2}
\] |
[_separable] |
✓ |
2.387 |
|
|
\[
{}x^{2} y^{\prime } = x y+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.403 |
|
|
\[
{}6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
454.237 |
|
|
\[
{}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{4}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.104 |
|
|
\[
{}x^{3} y^{\prime } = x^{2} y-y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
73.185 |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.814 |
|
|
\[
{}y^{\prime } = x^{2}-2 x y+y^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.773 |
|
|
\[
{}{\mathrm e}^{x}+y \,{\mathrm e}^{x y}+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.326 |
|
|
\[
{}2 x^{2} y-x^{3} y^{\prime } = y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
76.950 |
|
|
\[
{}3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2}
\] |
[_separable] |
✓ |
1.928 |
|
|
\[
{}x y^{\prime }+3 y = \frac {3}{x^{{3}/{2}}}
\] |
[_linear] |
✓ |
1.988 |
|
|
\[
{}\left (-1+x \right ) y+\left (x^{2}-1\right ) y^{\prime } = 1
\] |
[_linear] |
✓ |
1.385 |
|
|
\[
{}x y^{\prime } = 12 x^{4} y^{{2}/{3}}+6 y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
5.748 |
|
|
\[
{}{\mathrm e}^{y}+y \cos \left (x \right )+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
38.583 |
|
|
\[
{}9 y^{2} x^{2}+x^{{3}/{2}} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
1.941 |
|
|
\[
{}2 y+\left (x +1\right ) y^{\prime } = 3+3 x
\] |
[_linear] |
✓ |
1.933 |
|
|
\[
{}9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
0.281 |
|
|
\[
{}3 y+x^{3} y^{4}+3 x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.747 |
|
|
\[
{}x y^{\prime }+y = 2 \,{\mathrm e}^{2 x}
\] |
[_linear] |
✓ |
1.215 |
|
|
\[
{}y+\left (2 x +1\right ) y^{\prime } = \left (2 x +1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
3.808 |
|
|
\[
{}y^{\prime } = 3 x^{2} \left (7+y\right )
\] |
[_separable] |
✓ |
1.508 |
|