|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = 2 x y^{2}+3 x^{2} y^{2}
\] |
[_separable] |
✓ |
2.937 |
|
|
\[
{}y^{\prime } = 6 \,{\mathrm e}^{2 x -y}
\] |
[_separable] |
✓ |
8.050 |
|
|
\[
{}2 \sqrt {x}\, y^{\prime } = \cos \left (y\right )^{2}
\] |
[_separable] |
✓ |
4.745 |
|
|
\[
{}y^{\prime }+y = 2
\] |
[_quadrature] |
✓ |
1.429 |
|
|
\[
{}-2 y+y^{\prime } = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.458 |
|
|
\[
{}y^{\prime }+3 y = 2 x \,{\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
3.398 |
|
|
\[
{}y^{\prime }-2 x y = {\mathrm e}^{x^{2}}
\] |
[_linear] |
✓ |
1.359 |
|
|
\[
{}2 y+y^{\prime } x = 3 x
\] |
[_linear] |
✓ |
6.139 |
|
|
\[
{}2 y^{\prime } x +y = 10 \sqrt {x}
\] |
[_linear] |
✓ |
4.917 |
|
|
\[
{}2 y^{\prime } x +y = 10 \sqrt {x}
\] |
[_linear] |
✓ |
8.195 |
|
|
\[
{}y+3 y^{\prime } x = 12 x
\] |
[_linear] |
✓ |
2.447 |
|
|
\[
{}y^{\prime } x -y = x
\] |
[_linear] |
✓ |
4.557 |
|
|
\[
{}-3 y+2 y^{\prime } x = 9 x^{3}
\] |
[_linear] |
✓ |
3.130 |
|
|
\[
{}y^{\prime } x +y = 3 x y
\] |
[_separable] |
✓ |
3.712 |
|
|
\[
{}3 y+y^{\prime } x = 2 x^{5}
\] |
[_linear] |
✓ |
2.361 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.623 |
|
|
\[
{}-3 y+y^{\prime } x = x^{3}
\] |
[_linear] |
✓ |
2.365 |
|
|
\[
{}2 x y+y^{\prime } = x
\] |
[_separable] |
✓ |
1.770 |
|
|
\[
{}y^{\prime } = \cos \left (x \right ) \left (1-y\right )
\] |
[_separable] |
✓ |
4.485 |
|
|
\[
{}y+\left (x +1\right ) y^{\prime } = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.788 |
|
|
\[
{}y^{\prime } x = 2 y+x^{3} \cos \left (x \right )
\] |
[_linear] |
✓ |
1.948 |
|
|
\[
{}\cot \left (x \right ) y+y^{\prime } = \cos \left (x \right )
\] |
[_linear] |
✓ |
2.532 |
|
|
\[
{}y^{\prime } = 1+x +y+x y
\] |
[_separable] |
✓ |
2.824 |
|
|
\[
{}y^{\prime } x = x^{4} \cos \left (x \right )+3 y
\] |
[_linear] |
✓ |
4.235 |
|
|
\[
{}y^{\prime } = 3 \,{\mathrm e}^{x^{2}} x^{2}+2 x y
\] |
[_linear] |
✓ |
2.715 |
|
|
\[
{}\left (2 x -3\right ) y+y^{\prime } x = 4 x^{4}
\] |
[_linear] |
✓ |
3.512 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime }+3 x y = x
\] |
[_separable] |
✓ |
3.494 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+3 x^{3} y = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}}
\] |
[_linear] |
✓ |
2.628 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = x -y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
28.830 |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
21.606 |
|
|
\[
{}y^{\prime } x = y+2 \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
20.215 |
|
|
\[
{}\left (x -y\right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.586 |
|
|
\[
{}x \left (x +y\right ) y^{\prime } = y \left (x -y\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
11.987 |
|
|
\[
{}\left (x +2 y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
9.631 |
|
|
\[
{}x y^{2} y^{\prime } = x^{3}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
9.523 |
|
|
\[
{}x^{2} y^{\prime } = x y+x^{2} {\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
29.250 |
|
|
\[
{}x^{2} y^{\prime } = x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.358 |
|
|
\[
{}x y y^{\prime } = x^{2}+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.505 |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
9.159 |
|
|
\[
{}x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
148.174 |
|
|
\[
{}y^{\prime } x = y+\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
9.528 |
|
|
\[
{}x +y y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.592 |
|
|
\[
{}x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
16.880 |
|
|
\[
{}y^{\prime } = \sqrt {1+x +y}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
11.036 |
|
|
\[
{}y^{\prime } = \left (4 x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.846 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
1.482 |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 5 y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
8.054 |
|
|
\[
{}2 x y^{3}+y^{2} y^{\prime } = 6 x
\] |
[_separable] |
✓ |
2.033 |
|
|
\[
{}y^{\prime } = y+y^{3}
\] |
[_quadrature] |
✓ |
28.251 |
|
|
\[
{}2 x y+x^{2} y^{\prime } = 5 y^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.041 |
|
|
\[
{}6 y+y^{\prime } x = 3 x y^{{4}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
71.675 |
|
|
\[
{}y^{3} {\mathrm e}^{-2 x}+2 y^{\prime } x = 2 x y
\] |
[_Bernoulli] |
✓ |
5.521 |
|
|
\[
{}\sqrt {x^{4}+1}\, y^{2} \left (y^{\prime } x +y\right ) = x
\] |
[_Bernoulli] |
✓ |
6.198 |
|
|
\[
{}y^{3}+3 y^{2} y^{\prime } = {\mathrm e}^{-x}
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.928 |
|
|
\[
{}3 x y^{2} y^{\prime } = 3 x^{4}+y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.053 |
|
|
\[
{}{\mathrm e}^{y} x y^{\prime } = 2 \,{\mathrm e}^{y}+2 \,{\mathrm e}^{2 x} x^{3}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.072 |
|
|
\[
{}2 x \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 4 x^{2}+\sin \left (y\right )^{2}
\] |
[‘y=_G(x,y’)‘] |
✓ |
5.263 |
|
|
\[
{}\left ({\mathrm e}^{y}+x \right ) y^{\prime } = x \,{\mathrm e}^{-y}-1
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
5.796 |
|
|
\[
{}2 x +3 y+\left (3 x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
20.714 |
|
|
\[
{}4 x -y+\left (-x +6 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.276 |
|
|
\[
{}3 x^{2}+2 y^{2}+\left (4 x y+6 y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
8.000 |
|
|
\[
{}3 x^{2}+2 x y^{2}+\left (2 x^{2} y+4 y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
2.326 |
|
|
\[
{}x^{3}+\frac {y}{x}+\left (y^{2}+\ln \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
2.475 |
|
|
\[
{}1+{\mathrm e}^{x y} y+\left (2 y+x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
3.312 |
|
|
\[
{}\cos \left (x \right )+\ln \left (y\right )+\left (\frac {x}{y}+{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
7.105 |
|
|
\[
{}x +\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}} = 0
\] |
[_exact] |
✓ |
2.668 |
|
|
\[
{}3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.888 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+\tan \left (y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )+x \sec \left (y\right )^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
13.352 |
|
|
\[
{}\frac {2 x}{y}-\frac {3 y^{2}}{x^{4}}+\left (-\frac {x^{2}}{y^{2}}+\frac {1}{\sqrt {y}}+\frac {2 y}{x^{3}}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
15.704 |
|
|
\[
{}\frac {2 x^{{5}/{2}}-3 y^{{5}/{3}}}{2 x^{{5}/{2}} y^{{2}/{3}}}+\frac {\left (-2 x^{{5}/{2}}+3 y^{{5}/{3}}\right ) y^{\prime }}{3 x^{{3}/{2}} y^{{5}/{3}}} = 0
\] |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
6.241 |
|
|
\[
{}x^{3}+3 y-y^{\prime } x = 0
\] |
[_linear] |
✓ |
2.072 |
|
|
\[
{}3 y^{2}+x y^{2}-x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.510 |
|
|
\[
{}x y+y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.349 |
|
|
\[
{}{\mathrm e}^{x}+2 x y^{3}+\left (3 x^{2} y^{2}+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
4.266 |
|
|
\[
{}3 y+x^{4} y^{\prime } = 2 x y
\] |
[_separable] |
✓ |
3.817 |
|
|
\[
{}2 x y^{2}+x^{2} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
2.710 |
|
|
\[
{}2 x^{2} y+x^{3} y^{\prime } = 1
\] |
[_linear] |
✓ |
1.521 |
|
|
\[
{}2 x y+x^{2} y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
9.008 |
|
|
\[
{}2 y+y^{\prime } x = 6 x^{2} \sqrt {y}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
18.965 |
|
|
\[
{}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{2}
\] |
[_separable] |
✓ |
2.537 |
|
|
\[
{}x^{2} y^{\prime } = x y+3 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.508 |
|
|
\[
{}6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
18.678 |
|
|
\[
{}y^{\prime } = 1+x^{2}+y^{2}+x^{2} y^{4}
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.512 |
|
|
\[
{}x^{3} y^{\prime } = x^{2} y-y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
666.657 |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.171 |
|
|
\[
{}y^{\prime } = x^{2}-2 x y+y^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
3.912 |
|
|
\[
{}{\mathrm e}^{x}+{\mathrm e}^{x y} y+\left ({\mathrm e}^{y}+x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
4.213 |
|
|
\[
{}2 x^{2} y-x^{3} y^{\prime } = y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
678.381 |
|
|
\[
{}3 x^{5} y^{2}+x^{3} y^{\prime } = 2 y^{2}
\] |
[_separable] |
✓ |
2.884 |
|
|
\[
{}3 y+y^{\prime } x = \frac {3}{x^{{3}/{2}}}
\] |
[_linear] |
✓ |
6.836 |
|
|
\[
{}\left (x -1\right ) y+\left (x^{2}-1\right ) y^{\prime } = 1
\] |
[_linear] |
✓ |
1.695 |
|
|
\[
{}y^{\prime } x = 12 x^{4} y^{{2}/{3}}+6 y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
5.650 |
|
|
\[
{}{\mathrm e}^{y}+y \cos \left (x \right )+\left (x \,{\mathrm e}^{y}+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
40.308 |
|
|
\[
{}9 x^{2} y^{2}+x^{{3}/{2}} y^{\prime } = y^{2}
\] |
[_separable] |
✓ |
2.937 |
|
|
\[
{}2 y+\left (x +1\right ) y^{\prime } = 3+3 x
\] |
[_linear] |
✓ |
6.575 |
|
|
\[
{}9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
0.260 |
|
|
\[
{}3 y+x^{3} y^{4}+3 y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.546 |
|
|
\[
{}y^{\prime } x +y = 2 \,{\mathrm e}^{2 x}
\] |
[_linear] |
✓ |
1.591 |
|
|
\[
{}y+\left (2 x +1\right ) y^{\prime } = \left (2 x +1\right )^{{3}/{2}}
\] |
[_linear] |
✓ |
11.485 |
|
|
\[
{}y^{\prime } = 3 \left (y+7\right ) x^{2}
\] |
[_separable] |
✓ |
3.895 |
|