|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y y^{\prime }+1+y^{2} = 0
\] |
[_separable] |
✓ |
2.487 |
|
|
\[
{}x y y^{\prime } = x +y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.361 |
|
|
\[
{}x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.983 |
|
|
\[
{}x y y^{\prime }+x^{4}-y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.406 |
|
|
\[
{}x y y^{\prime } = a \,x^{3} \cos \left (x \right )+y^{2}
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
3.250 |
|
|
\[
{}x y y^{\prime } = x^{2}-x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.773 |
|
|
\[
{}x y y^{\prime }+2 x^{2}-2 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.017 |
|
|
\[
{}x y y^{\prime } = a +b y^{2}
\] |
[_separable] |
✓ |
1.921 |
|
|
\[
{}x y y^{\prime } = a \,x^{n}+b y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.842 |
|
|
\[
{}x y y^{\prime } = \left (x^{2}+1\right ) \left (1-y^{2}\right )
\] |
[_separable] |
✓ |
2.274 |
|
|
\[
{}x y y^{\prime }+x^{2} \operatorname {arccot}\left (\frac {y}{x}\right )-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
8.113 |
|
|
\[
{}x y y^{\prime }+x^{2} {\mathrm e}^{-\frac {2 y}{x}}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.180 |
|
|
\[
{}\left (x y+1\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.641 |
|
|
\[
{}x \left (1+y\right ) y^{\prime }-\left (1-x \right ) y = 0
\] |
[_separable] |
✓ |
1.306 |
|
|
\[
{}x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y = 0
\] |
[_separable] |
✓ |
1.428 |
|
|
\[
{}x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[_separable] |
✓ |
1.404 |
|
|
\[
{}x \left (2+y\right ) y^{\prime }+a x = 0
\] |
[_quadrature] |
✓ |
0.748 |
|
|
\[
{}\left (2+3 x -x y\right ) y^{\prime }+y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.112 |
|
|
\[
{}x \left (4+y\right ) y^{\prime } = 2 x +2 y+y^{2}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.915 |
|
|
\[
{}x \left (a +y\right ) y^{\prime }+b x +c y = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.877 |
|
|
\[
{}x \left (a +y\right ) y^{\prime } = y \left (B x +A \right )
\] |
[_separable] |
✓ |
1.385 |
|
|
\[
{}x \left (x +y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.788 |
|
|
\[
{}x \left (x -y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
37.446 |
|
|
\[
{}x \left (x +y\right ) y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.383 |
|
|
\[
{}x \left (x -y\right ) y^{\prime }+2 x^{2}+3 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.734 |
|
|
\[
{}x \left (x +y\right ) y^{\prime }-y \left (x +y\right )+x \sqrt {x^{2}-y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.711 |
|
|
\[
{}\left (a +\left (x +y\right ) x \right ) y^{\prime } = b \left (x +y\right ) y
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.213 |
|
|
\[
{}x \left (y+2 x \right ) y^{\prime } = x^{2}+x y-y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.694 |
|
|
\[
{}x \left (4 x -y\right ) y^{\prime }+4 x^{2}-6 x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.660 |
|
|
\[
{}x \left (x^{3}+y\right ) y^{\prime } = \left (x^{3}-y\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.080 |
|
|
\[
{}x \left (2 x^{3}+y\right ) y^{\prime } = \left (2 x^{3}-y\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.944 |
|
|
\[
{}x \left (2 x^{3}+y\right ) y^{\prime } = 6 y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.505 |
|
|
\[
{}y \left (1-x \right ) y^{\prime }+x \left (1-y\right ) = 0
\] |
[_separable] |
✓ |
1.217 |
|
|
\[
{}\left (x +a \right ) \left (x +b \right ) y^{\prime } = x y
\] |
[_separable] |
✓ |
1.424 |
|
|
\[
{}2 x y y^{\prime }+1-2 x^{3}-y^{2} = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.414 |
|
|
\[
{}2 x y y^{\prime }+a +y^{2} = 0
\] |
[_separable] |
✓ |
1.601 |
|
|
\[
{}2 x y y^{\prime } = a x +y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.274 |
|
|
\[
{}2 x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
4.554 |
|
|
\[
{}2 x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.708 |
|
|
\[
{}2 x y y^{\prime } = 4 x^{2} \left (2 x +1\right )+y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
2.276 |
|
|
\[
{}2 x y y^{\prime }+x^{2} \left (a \,x^{3}+1\right ) = 6 y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
1.351 |
|
|
\[
{}\left (3-x +2 x y\right ) y^{\prime }+3 x^{2}-y+y^{2} = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.567 |
|
|
\[
{}x \left (x -2 y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
14.065 |
|
|
\[
{}x \left (x +2 y\right ) y^{\prime }+\left (2 x -y\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
67.428 |
|
|
\[
{}x \left (x -2 y\right ) y^{\prime }+\left (2 x -y\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.940 |
|
|
\[
{}x \left (1+x -2 y\right ) y^{\prime }+\left (1-2 x +y\right ) y = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.407 |
|
|
\[
{}x \left (1-x -2 y\right ) y^{\prime }+\left (1+2 x +y\right ) y = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.417 |
|
|
\[
{}2 x \left (2 x^{2}+y\right ) y^{\prime }+\left (12 x^{2}+y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.138 |
|
|
\[
{}2 \left (x +1\right ) y y^{\prime }+2 x -3 x^{2}+y^{2} = 0
\] |
[_exact, _rational, _Bernoulli] |
✓ |
1.730 |
|
|
\[
{}x \left (2 x +3 y\right ) y^{\prime } = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.092 |
|
|
\[
{}x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.008 |
|
|
\[
{}\left (3+6 x y+x^{2}\right ) y^{\prime }+2 x +2 x y+3 y^{2} = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.389 |
|
|
\[
{}3 x \left (x +2 y\right ) y^{\prime }+x^{3}+3 y \left (y+2 x \right ) = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.437 |
|
|
\[
{}a x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.047 |
|
|
\[
{}a x y y^{\prime }+x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.871 |
|
|
\[
{}x \left (a +b y\right ) y^{\prime } = c y
\] |
[_separable] |
✓ |
1.360 |
|
|
\[
{}x \left (x -a y\right ) y^{\prime } = y \left (y-a x \right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.352 |
|
|
\[
{}x \left (x^{n}+a y\right ) y^{\prime }+\left (b +c y\right ) y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
4.651 |
|
|
\[
{}\left (1-x^{2} y\right ) y^{\prime }+1-x y^{2} = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.245 |
|
|
\[
{}\left (1-x^{2} y\right ) y^{\prime }-1+x y^{2} = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.779 |
|
|
\[
{}x \left (1-x y\right ) y^{\prime }+\left (x y+1\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.742 |
|
|
\[
{}x \left (2+x y\right ) y^{\prime } = 3+2 x^{3}-2 y-x y^{2}
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.562 |
|
|
\[
{}x \left (2-x y\right ) y^{\prime }+2 y-x y^{2} \left (x y+1\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.525 |
|
|
\[
{}x \left (3-x y\right ) y^{\prime } = y \left (x y-1\right )
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.197 |
|
|
\[
{}x^{2} \left (1-y\right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[_separable] |
✓ |
1.569 |
|
|
\[
{}x^{2} \left (1-y\right ) y^{\prime }+\left (x +1\right ) y^{2} = 0
\] |
[_separable] |
✓ |
1.669 |
|
|
\[
{}\left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right ) = 0
\] |
[_separable] |
✓ |
4.275 |
|
|
\[
{}\left (-x^{2}+1\right ) y y^{\prime }+2 x^{2}+x y^{2} = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.664 |
|
|
\[
{}2 x^{2} y y^{\prime } = x^{2} \left (2 x +1\right )-y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.233 |
|
|
\[
{}x \left (1-2 x y\right ) y^{\prime }+\left (1+2 x y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.777 |
|
|
\[
{}x \left (1+2 x y\right ) y^{\prime }+\left (2+3 x y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.013 |
|
|
\[
{}x \left (1+2 x y\right ) y^{\prime }+\left (1+2 x y-x^{2} y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.531 |
|
|
\[
{}x^{2} \left (x -2 y\right ) y^{\prime } = 2 x^{3}-4 x y^{2}+y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
47.083 |
|
|
\[
{}2 \left (x +1\right ) x y y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
2.624 |
|
|
\[
{}3 x^{2} y y^{\prime }+1+2 x y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.365 |
|
|
\[
{}x^{2} \left (4 x -3 y\right ) y^{\prime } = \left (6 x^{2}-3 x y+2 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
10.118 |
|
|
\[
{}\left (1-x^{3} y\right ) y^{\prime } = x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.558 |
|
|
\[
{}2 x^{3} y y^{\prime }+a +3 x^{2} y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
1.491 |
|
|
\[
{}x \left (3-2 x^{2} y\right ) y^{\prime } = 4 x -3 y+3 x^{2} y^{2}
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.466 |
|
|
\[
{}x \left (3+2 x^{2} y\right ) y^{\prime }+\left (4+3 x^{2} y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.378 |
|
|
\[
{}8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.590 |
|
|
\[
{}x y \left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2}
\] |
[_separable] |
✓ |
3.235 |
|
|
\[
{}3 x^{4} y y^{\prime } = 1-2 x^{3} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.483 |
|
|
\[
{}x^{7} y y^{\prime } = 2 x^{2}+2+5 x^{3} y
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.941 |
|
|
\[
{}y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}} = 0
\] |
[_separable] |
✓ |
2.715 |
|
|
\[
{}\left (1+y\right ) y^{\prime } \sqrt {x^{2}+1} = y^{3}
\] |
[_separable] |
✓ |
2.275 |
|
|
\[
{}\left (\operatorname {g0} \left (x \right )+y \operatorname {g1} \left (x \right )\right ) y^{\prime } = \operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3}
\] |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
4.505 |
|
|
\[
{}y^{2} y^{\prime }+x \left (2-y\right ) = 0
\] |
[_separable] |
✓ |
1.292 |
|
|
\[
{}y^{2} y^{\prime } = x \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
1.441 |
|
|
\[
{}\left (x +y^{2}\right ) y^{\prime }+y = b x +a
\] |
[_exact, _rational] |
✓ |
1.233 |
|
|
\[
{}\left (x -y^{2}\right ) y^{\prime } = x^{2}-y
\] |
[_exact, _rational] |
✓ |
1.152 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime }+x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.219 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.372 |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.602 |
|
|
\[
{}\left (x^{2}-y^{2}\right ) y^{\prime }+x \left (x +2 y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
94.251 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
4.472 |
|
|
\[
{}\left (1-x^{2}+y^{2}\right ) y^{\prime } = 1+x^{2}-y^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.102 |
|
|
\[
{}\left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+2 x y = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.002 |
|
|
\[
{}\left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+b^{2}+x^{2}+2 x y = 0
\] |
[_exact, _rational] |
✓ |
1.235 |
|
|
\[
{}\left (x +x^{2}+y^{2}\right ) y^{\prime } = y
\] |
[_rational] |
✓ |
1.170 |
|