|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x \left (x -1\right ) y^{\prime }+\left (x -1\right ) y^{2}-x = 0
\] |
[_rational, _Riccati] |
✓ |
1.994 |
|
|
\[
{}3 x^{2} y^{\prime }-7 y^{2}-3 y x -x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.372 |
|
|
\[
{}3 \left (x^{2}-4\right ) y^{\prime }+y^{2}-y x -3 = 0
\] |
[_rational, _Riccati] |
✓ |
149.910 |
|
|
\[
{}\left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
1.312 |
|
|
\[
{}x^{3} y^{\prime }-y^{2}-x^{4} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.122 |
|
|
\[
{}x^{3} y^{\prime }-y^{2}-x^{2} y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.769 |
|
|
\[
{}x^{3} y^{\prime }-x^{4} y^{2}+x^{2} y+20 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.771 |
|
|
\[
{}x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3 = 0
\] |
[_rational, _Riccati] |
✓ |
1.647 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime }+x^{2} y = 0
\] |
[_separable] |
✓ |
1.202 |
|
|
\[
{}x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3} = 0
\] |
[_linear] |
✓ |
1.099 |
|
|
\[
{}x \left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right ) y^{2}-x^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
64.327 |
|
|
\[
{}x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.062 |
|
|
\[
{}2 x \left (x^{2}-1\right ) y^{\prime }+2 \left (x^{2}-1\right ) y^{2}-\left (3 x^{2}-5\right ) y+x^{2}-3 = 0
\] |
[_rational, _Riccati] |
✓ |
1.928 |
|
|
\[
{}3 x \left (x^{2}-1\right ) y^{\prime }+x y^{2}-\left (x^{2}+1\right ) y-3 x = 0
\] |
[_rational, _Riccati] |
✓ |
13.943 |
|
|
\[
{}\left (a \,x^{2}+b x +c \right ) \left (-y+y^{\prime } x \right )-y^{2}+x^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.773 |
|
|
\[
{}x^{4} \left (y^{\prime }+y^{2}\right )+a = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
1.285 |
|
|
\[
{}x \left (x^{3}-1\right ) y^{\prime }-2 x y^{2}+y+x^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
1.612 |
|
|
\[
{}\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y = 0
\] |
[_separable] |
✓ |
1.290 |
|
|
\[
{}\left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\] |
[_rational, _Riccati] |
✓ |
3.755 |
|
|
\[
{}x^{7} y^{\prime }+2 \left (x^{2}+1\right ) y^{3}+5 x^{3} y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.646 |
|
|
\[
{}x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{2 n -2} = 0
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
2.302 |
|
|
\[
{}x^{n} y^{\prime }-a y^{2}-b \,x^{2 n -2} = 0
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
3.753 |
|
|
\[
{}x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n} = 0
\] |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
7.615 |
|
|
\[
{}x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (m +1\right )} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.582 |
|
|
\[
{}\sqrt {x^{2}-1}\, y^{\prime }-\sqrt {-1+y^{2}} = 0
\] |
[_separable] |
✓ |
8.312 |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{\prime }-y \sqrt {-1+y^{2}} = 0
\] |
[_separable] |
✓ |
6.712 |
|
|
\[
{}\sqrt {a^{2}+x^{2}}\, y^{\prime }+y-\sqrt {a^{2}+x^{2}}+x = 0
\] |
[_linear] |
✓ |
1.482 |
|
|
\[
{}x y^{\prime } \ln \left (x \right )+y-a x \left (1+\ln \left (x \right )\right ) = 0
\] |
[_linear] |
✓ |
1.307 |
|
|
\[
{}x y^{\prime } \ln \left (x \right )-y^{2} \ln \left (x \right )-\left (2 \ln \left (x \right )^{2}+1\right ) y-\ln \left (x \right )^{3} = 0
\] |
[_Riccati] |
✓ |
2.467 |
|
|
\[
{}\sin \left (x \right ) y^{\prime }-y^{2} \sin \left (x \right )^{2}+\left (\cos \left (x \right )-3 \sin \left (x \right )\right ) y+4 = 0
\] |
[_Riccati] |
✓ |
12.989 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.972 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }-y^{4}-\sin \left (x \right ) y = 0
\] |
[_Bernoulli] |
✓ |
9.444 |
|
|
\[
{}\sin \left (x \right ) \cos \left (x \right ) y^{\prime }-y-\sin \left (x \right )^{3} = 0
\] |
[_linear] |
✓ |
5.224 |
|
|
\[
{}y^{\prime } \sin \left (2 x \right )+\sin \left (2 y\right ) = 0
\] |
[_separable] |
✓ |
28.791 |
|
|
\[
{}\left (a \sin \left (x \right )^{2}+b \right ) y^{\prime }+a y \sin \left (2 x \right )+A x \left (a \sin \left (x \right )^{2}+c \right ) = 0
\] |
[_linear] |
✓ |
19.899 |
|
|
\[
{}2 f \left (x \right ) y^{\prime }+2 f \left (x \right ) y^{2}-f^{\prime }\left (x \right ) y-2 f \left (x \right )^{2} = 0
\] |
[_Riccati] |
✓ |
1.035 |
|
|
\[
{}f \left (x \right ) y^{\prime }+g \left (x \right ) s \left (y\right )+h \left (x \right ) = 0
\] |
[NONE] |
✗ |
0.871 |
|
|
\[
{}y y^{\prime }+y+x^{3} = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.330 |
|
|
\[
{}y y^{\prime }+a y+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.296 |
|
|
\[
{}y y^{\prime }+a y+\frac {\left (a^{2}-1\right ) x}{4}+b \,x^{n} = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.968 |
|
|
\[
{}y y^{\prime }+a y+b \,{\mathrm e}^{x}-2 a = 0
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.852 |
|
|
\[
{}y y^{\prime }+y^{2}+4 x \left (x +1\right ) = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.820 |
|
|
\[
{}y y^{\prime }+a y^{2}-b \cos \left (x +c \right ) = 0
\] |
[_Bernoulli] |
✓ |
3.037 |
|
|
\[
{}y y^{\prime }-\sqrt {a y^{2}+b} = 0
\] |
[_quadrature] |
✓ |
1.750 |
|
|
\[
{}y y^{\prime }+x y^{2}-4 x = 0
\] |
[_separable] |
✓ |
1.911 |
|
|
\[
{}y y^{\prime }-x \,{\mathrm e}^{\frac {x}{y}} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.171 |
|
|
\[
{}y y^{\prime }+f \left (x^{2}+y^{2}\right ) g \left (x \right )+x = 0
\] |
[NONE] |
✗ |
1.418 |
|
|
\[
{}\left (1+y\right ) y^{\prime }-y-x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.123 |
|
|
\[
{}\left (y+x -1\right ) y^{\prime }-y+2 x +3 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.518 |
|
|
\[
{}\left (y+2 x -2\right ) y^{\prime }-y+x +1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.790 |
|
|
\[
{}\left (y-2 x +1\right ) y^{\prime }+y+x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.847 |
|
|
\[
{}\left (y-x^{2}\right ) y^{\prime }-x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
0.915 |
|
|
\[
{}\left (y-x^{2}\right ) y^{\prime }+4 y x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.835 |
|
|
\[
{}\left (y+g \left (x \right )\right ) y^{\prime }-f_{2} \left (x \right ) y^{2}-f_{1} \left (x \right ) y-f_{0} \left (x \right ) = 0
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
7.083 |
|
|
\[
{}2 y y^{\prime }-x y^{2}-x^{3} = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.242 |
|
|
\[
{}\left (2 y+x +1\right ) y^{\prime }-2 y-x +1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.233 |
|
|
\[
{}\left (2 y+x +7\right ) y^{\prime }-y+2 x +4 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.718 |
|
|
\[
{}\left (2 y-x \right ) y^{\prime }-y-2 x = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.171 |
|
|
\[
{}\left (2 y-6 x \right ) y^{\prime }-y+3 x +2 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.295 |
|
|
\[
{}\left (4 y+2 x +3\right ) y^{\prime }-2 y-x -1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.240 |
|
|
\[
{}\left (4 y-2 x -3\right ) y^{\prime }+2 y-x -1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.220 |
|
|
\[
{}\left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.532 |
|
|
\[
{}\left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.320 |
|
|
\[
{}\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.616 |
|
|
\[
{}a y y^{\prime }+b y^{2}+f \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
2.083 |
|
|
\[
{}\left (a y+b x +c \right ) y^{\prime }+\alpha y+\beta x +\gamma = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.527 |
|
|
\[
{}x y y^{\prime }+y^{2}+x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.402 |
|
|
\[
{}x y y^{\prime }-y^{2}+a \,x^{3} \cos \left (x \right ) = 0
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
3.884 |
|
|
\[
{}x y y^{\prime }-y^{2}+y x +x^{3}-2 x^{2} = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.510 |
|
|
\[
{}\left (y x +a \right ) y^{\prime }+b y = 0
\] |
[[_1st_order, _with_exponential_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.914 |
|
|
\[
{}x \left (y+4\right ) y^{\prime }-y^{2}-2 y-2 x = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.425 |
|
|
\[
{}x \left (y+a \right ) y^{\prime }+b y+c x = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.483 |
|
|
\[
{}\left (x \left (x +y\right )+a \right ) y^{\prime }-y \left (x +y\right )-b = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.372 |
|
|
\[
{}\left (y x -x^{2}\right ) y^{\prime }+y^{2}-3 y x -2 x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.217 |
|
|
\[
{}2 x y y^{\prime }-y^{2}+a x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.200 |
|
|
\[
{}2 x y y^{\prime }-y^{2}+a \,x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.965 |
|
|
\[
{}2 x y y^{\prime }+2 y^{2}+1 = 0
\] |
[_separable] |
✓ |
1.899 |
|
|
\[
{}x \left (2 y+x -1\right ) y^{\prime }-y \left (2 x +y+1\right ) = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.374 |
|
|
\[
{}x \left (2 y-x -1\right ) y^{\prime }+y \left (2 x -y-1\right ) = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.349 |
|
|
\[
{}\left (2 y x +4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.184 |
|
|
\[
{}x \left (3 y+2 x \right ) y^{\prime }+3 \left (x +y\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
7.395 |
|
|
\[
{}\left (2+3 x \right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+y x -7 x^{2}-9 x -3 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.477 |
|
|
\[
{}\left (6 y x +x^{2}+3\right ) y^{\prime }+3 y^{2}+2 y x +2 x = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.258 |
|
|
\[
{}\left (a x y+b \,x^{n}\right ) y^{\prime }+\alpha y^{3}+\beta y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
5.555 |
|
|
\[
{}\left (B x y+A \,x^{2}+a x +b y+c \right ) y^{\prime }-B g \left (x \right )^{2}+A x y+\alpha x +\beta y+\gamma = 0
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
4.056 |
|
|
\[
{}\left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1 = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.244 |
|
|
\[
{}\left (x^{2} y-1\right ) y^{\prime }+1-x y^{2} = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.923 |
|
|
\[
{}\left (x^{2} y-1\right ) y^{\prime }-8+8 x y^{2} = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.613 |
|
|
\[
{}x \left (y x -2\right ) y^{\prime }+x^{2} y^{3}+x y^{2}-2 y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.307 |
|
|
\[
{}x \left (y x -3\right ) y^{\prime }+x y^{2}-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.818 |
|
|
\[
{}x^{2} \left (-1+y\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[_separable] |
✓ |
1.555 |
|
|
\[
{}x \left (y x +x^{4}-1\right ) y^{\prime }-y \left (y x -x^{4}-1\right ) = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.756 |
|
|
\[
{}2 x^{2} y y^{\prime }+y^{2}-2 x^{3}-x^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.122 |
|
|
\[
{}2 x^{2} y y^{\prime }-y^{2}-x^{2} {\mathrm e}^{x -\frac {1}{x}} = 0
\] |
[_Bernoulli] |
✓ |
2.168 |
|
|
\[
{}\left (2 x^{2} y+x \right ) y^{\prime }-x^{2} y^{3}+2 x y^{2}+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.433 |
|
|
\[
{}\left (2 x^{2} y-x \right ) y^{\prime }-2 x y^{2}-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.701 |
|
|
\[
{}\left (2 x^{2} y-x^{3}\right ) y^{\prime }+y^{3}-4 x y^{2}+2 x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
33.616 |
|
|
\[
{}2 x^{3}+y y^{\prime }+3 x^{2} y^{2}+7 = 0
\] |
[_rational, _Bernoulli] |
✓ |
2.432 |
|
|
\[
{}2 x \left (x^{3} y+1\right ) y^{\prime }+\left (3 x^{3} y-1\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.151 |
|
|
\[
{}\left (x^{n \left (n +1\right )} y-1\right ) y^{\prime }+2 \left (n +1\right )^{2} x^{n -1} \left (x^{n^{2}} y^{2}-1\right ) = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.638 |
|