|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 2 x y^{2}+3 x^{2} y^{2}
\] |
[_separable] |
✓ |
1.794 |
|
|
\[
{}y^{\prime } = 6 \,{\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
3.030 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime } = \cos \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.099 |
|
|
\[
{}y^{\prime }+y = 2
\] |
[_quadrature] |
✓ |
1.215 |
|
|
\[
{}-2 y+y^{\prime } = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.291 |
|
|
\[
{}3 y+y^{\prime } = 2 x \,{\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.528 |
|
|
\[
{}y^{\prime }-2 x y = {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
1.371 |
|
|
\[
{}2 y+x y^{\prime } = 3 x
\] |
[_linear] |
✓ |
2.624 |
|
|
\[
{}y+2 x y^{\prime } = 10 \sqrt {x}
\] |
[_linear] |
✓ |
4.753 |
|
|
\[
{}y+2 x y^{\prime } = 10 \sqrt {x}
\] |
[_linear] |
✓ |
3.926 |
|
|
\[
{}y+3 x y^{\prime } = 12 x
\] |
[_linear] |
✓ |
1.973 |
|
|
\[
{}x y^{\prime }-y = x
\] |
[_linear] |
✓ |
1.543 |
|
|
\[
{}-3 y+2 x y^{\prime } = 9 x^{3}
\] |
[_linear] |
✓ |
1.357 |
|
|
\[
{}y+x y^{\prime } = 3 x y
\] |
[_separable] |
✓ |
1.634 |
|
|
\[
{}3 y+x y^{\prime } = 2 x^{5}
\] |
[_linear] |
✓ |
1.760 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.354 |
|
|
\[
{}-3 y+x y^{\prime } = x^{3}
\] |
[_linear] |
✓ |
1.392 |
|
|
\[
{}2 x y+y^{\prime } = x
\] |
[_separable] |
✓ |
1.649 |
|
|
\[
{}y^{\prime } = \left (1-y\right ) \cos \left (x \right )
\] |
[_separable] |
✓ |
1.862 |
|
|
\[
{}y+\left (x +1\right ) y^{\prime } = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.769 |
|
|
\[
{}x y^{\prime } = x^{3} \cos \left (x \right )+2 y
\] |
[_linear] |
✓ |
1.806 |
|
|
\[
{}\cot \left (x \right ) y+y^{\prime } = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.827 |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
1.628 |
|
|
\[
{}x y^{\prime } = x^{4} \cos \left (x \right )+3 y
\] |
[_linear] |
✓ |
2.741 |
|
|
\[
{}y^{\prime } = 3 \,{\mathrm e}^{x^{2}} x^{2}+2 x y
\] |
[_linear] |
✓ |
2.835 |
|
|
\[
{}\left (2 x -3\right ) y+x y^{\prime } = 4 x^{4}
\] |
[_linear] |
✓ |
2.324 |
|
|
\[
{}3 x y+\left (x^{2}+4\right ) y^{\prime } = x
\] |
[_separable] |
✓ |
2.076 |
|
|
\[
{}3 x^{3} y+\left (x^{2}+1\right ) y^{\prime } = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}}
\] |
[_linear] |
✓ |
2.513 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = x -y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.938 |
|
|
\[
{}2 x y y^{\prime } = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
8.286 |
|
|
\[
{}x y^{\prime } = y+2 \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.793 |
|
|
\[
{}\left (x -y\right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.859 |
|
|
\[
{}x \left (x +y\right ) y^{\prime } = y \left (x -y\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.215 |
|
|
\[
{}\left (x +2 y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.548 |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
8.069 |
|
|
\[
{}x^{2} y^{\prime } = {\mathrm e}^{\frac {y}{x}} x^{2}+x y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.598 |
|
|
\[
{}x^{2} y^{\prime } = x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.950 |
|
|
\[
{}x y y^{\prime } = x^{2}+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.905 |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.537 |
|
|
\[
{}x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
26.792 |
|
|
\[
{}x y^{\prime } = y+\sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.972 |
|
|
\[
{}x +y y^{\prime } = \sqrt {y^{2}+x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.843 |
|
|
\[
{}y \left (3 x +y\right )+x \left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.857 |
|
|
\[
{}y^{\prime } = \sqrt {x +y+1}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.542 |
|
|
\[
{}y^{\prime } = \left (4 x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.666 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.408 |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 5 y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.813 |
|
|
\[
{}2 x y^{3}+y^{2} y^{\prime } = 6 x
\] |
[_separable] |
✓ |
1.889 |
|
|
\[
{}y^{\prime } = y+y^{3}
\] |
[_quadrature] |
✓ |
4.030 |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 5 y^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.931 |
|
|
\[
{}6 y+x y^{\prime } = 3 x y^{{4}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
54.468 |
|
|
\[
{}y^{3} {\mathrm e}^{-2 x}+2 x y^{\prime } = 2 x y
\] |
[_Bernoulli] |
✓ |
2.507 |
|
|
\[
{}\sqrt {x^{4}+1}\, y^{2} \left (y+x y^{\prime }\right ) = x
\] |
[_Bernoulli] |
✓ |
6.079 |
|
|
\[
{}y^{3}+3 y^{2} y^{\prime } = {\mathrm e}^{-x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.859 |
|
|
\[
{}3 x y^{2} y^{\prime } = 3 x^{4}+y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.023 |
|
|
\[
{}x \,{\mathrm e}^{y} y^{\prime } = 2 \,{\mathrm e}^{y}+2 \,{\mathrm e}^{2 x} x^{3}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.533 |
|
|
\[
{}2 x \cos \left (y\right ) \sin \left (y\right ) y^{\prime } = 4 x^{2}+\sin \left (y\right )^{2}
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.122 |
|
|
\[
{}\left ({\mathrm e}^{y}+x \right ) y^{\prime } = -1+x \,{\mathrm e}^{-y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.691 |
|
|
\[
{}2 x +3 y+\left (3 x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.886 |
|
|
\[
{}4 x -y+\left (6 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.398 |
|
|
\[
{}3 x^{2}+2 y^{2}+\left (4 x y+6 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
10.691 |
|
|
\[
{}3 x^{2}+2 x y^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.888 |
|
|
\[
{}x^{3}+\frac {y}{x}+\left (\ln \left (x \right )+y^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.509 |
|
|
\[
{}1+{\mathrm e}^{x y} y+\left (x \,{\mathrm e}^{x y}+2 y\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.973 |
|
|
\[
{}\cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.755 |
|
|
\[
{}x +\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}} = 0
\] |
[_exact] |
✓ |
1.703 |
|
|
\[
{}3 y^{3} x^{2}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.492 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
16.472 |
|
|
\[
{}\frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (\frac {2 y}{x^{3}}-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
10.704 |
|
|
\[
{}\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (3 y^{{5}/{3}}-2 x^{{5}/{2}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
2.070 |
|
|
\[
{}x^{3}+3 y-x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.030 |
|
|
\[
{}3 y^{2}+x y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.519 |
|
|
\[
{}x y+y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.846 |
|
|
\[
{}2 x y^{3}+{\mathrm e}^{x}+\left (3 x^{2} y^{2}+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.039 |
|
|
\[
{}3 y+x^{4} y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
1.553 |
|
|
\[
{}2 x y^{2}+x^{2} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
1.508 |
|
|
\[
{}2 x^{2} y+x^{3} y^{\prime } = 1
\] |
[_linear] |
✓ |
1.032 |
|
|
\[
{}2 x y+x^{2} y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.454 |
|
|
\[
{}2 y+x y^{\prime } = 6 x^{2} \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.400 |
|
|
\[
{}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{2}
\] |
[_separable] |
✓ |
2.134 |
|
|
\[
{}x^{2} y^{\prime } = x y+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.869 |
|
|
\[
{}6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.551 |
|
|
\[
{}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{4}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.096 |
|
|
\[
{}x^{3} y^{\prime } = x^{2} y-y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
81.421 |
|
|
\[
{}3 y+y^{\prime } = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.620 |
|
|
\[
{}y^{\prime } = x^{2}-2 x y+y^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.824 |
|
|
\[
{}{\mathrm e}^{x}+{\mathrm e}^{x y} y+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.280 |
|
|
\[
{}2 x^{2} y-x^{3} y^{\prime } = y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
124.797 |
|
|
\[
{}3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2}
\] |
[_separable] |
✓ |
1.448 |
|
|
\[
{}3 y+x y^{\prime } = \frac {3}{x^{{3}/{2}}}
\] |
[_linear] |
✓ |
1.674 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+\left (x -1\right ) y = 1
\] |
[_linear] |
✓ |
1.246 |
|
|
\[
{}x y^{\prime } = 12 x^{4} y^{{2}/{3}}+6 y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
4.788 |
|
|
\[
{}{\mathrm e}^{y}+y \cos \left (x \right )+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
36.792 |
|
|
\[
{}9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
1.668 |
|
|
\[
{}2 y+\left (x +1\right ) y^{\prime } = 3+3 x
\] |
[_linear] |
✓ |
1.509 |
|
|
\[
{}9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
0.275 |
|
|
\[
{}3 y+x^{3} y^{4}+3 x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.323 |
|
|
\[
{}y+x y^{\prime } = 2 \,{\mathrm e}^{2 x}
\] |
[_linear] |
✓ |
1.104 |
|
|
\[
{}y+\left (2 x +1\right ) y^{\prime } = \left (2 x +1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
3.659 |
|
|
\[
{}y^{\prime } = 3 x^{2} \left (y+7\right )
\] |
[_separable] |
✓ |
1.244 |
|