|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{\prime }-\sqrt {a^{2}-x^{2}} = 0
\] |
[_quadrature] |
✓ |
0.494 |
|
|
\[
{}x y^{\prime }+y-x \sin \left (x \right ) = 0
\] |
[_linear] |
✓ |
1.398 |
|
|
\[
{}x y^{\prime }-y-\frac {x}{\ln \left (x \right )} = 0
\] |
[_linear] |
✓ |
1.322 |
|
|
\[
{}x y^{\prime }-y-x^{2} \sin \left (x \right ) = 0
\] |
[_linear] |
✓ |
1.560 |
|
|
\[
{}x y^{\prime }-y-\frac {x \cos \left (\ln \left (\ln \left (x \right )\right )\right )}{\ln \left (x \right )} = 0
\] |
[_linear] |
✓ |
2.809 |
|
|
\[
{}x y^{\prime }+a y+b \,x^{n} = 0
\] |
[_linear] |
✓ |
1.207 |
|
|
\[
{}x y^{\prime }+y^{2}+x^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
1.139 |
|
|
\[
{}x y^{\prime }-y^{2}+1 = 0
\] |
[_separable] |
✓ |
1.781 |
|
|
\[
{}x y^{\prime }+a y^{2}-y+b \,x^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.430 |
|
|
\[
{}x y^{\prime }+a y^{2}-b y+c \,x^{2 b} = 0
\] |
[_rational, _Riccati] |
✓ |
2.785 |
|
|
\[
{}x y^{\prime }+a y^{2}-b y-c \,x^{\beta } = 0
\] |
[_rational, _Riccati] |
✓ |
2.373 |
|
|
\[
{}x y^{\prime }+x y^{2}+a = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
1.059 |
|
|
\[
{}x y^{\prime }+x y^{2}-y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.435 |
|
|
\[
{}x y^{\prime }+x y^{2}-y-a \,x^{3} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.646 |
|
|
\[
{}x y^{\prime }+x y^{2}-\left (2 x^{2}+1\right ) y-x^{3} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.873 |
|
|
\[
{}x y^{\prime }+a x y^{2}+2 y+b x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.131 |
|
|
\[
{}x y^{\prime }+a x y^{2}+b y+c x +d = 0
\] |
[_rational, _Riccati] |
✓ |
7.562 |
|
|
\[
{}x y^{\prime }+x^{a} y^{2}+\frac {\left (a -b \right ) y}{2}+x^{b} = 0
\] |
[_rational, _Riccati] |
✓ |
2.240 |
|
|
\[
{}x y^{\prime }+a \,x^{\alpha } y^{2}+b y-c \,x^{\beta } = 0
\] |
[_rational, _Riccati] |
✓ |
3.614 |
|
|
\[
{}x y^{\prime }-y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
2.411 |
|
|
\[
{}x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right ) = 0
\] |
[_Bernoulli] |
✓ |
2.510 |
|
|
\[
{}x y^{\prime }+f \left (x \right ) \left (y^{2}-x^{2}\right )-y = 0
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
1.951 |
|
|
\[
{}x y^{\prime }+y^{3}+3 x y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.821 |
|
|
\[
{}x y^{\prime }-\sqrt {x^{2}+y^{2}}-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.138 |
|
|
\[
{}x y^{\prime }+a \sqrt {x^{2}+y^{2}}-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
14.194 |
|
|
\[
{}x y^{\prime }-x \sqrt {x^{2}+y^{2}}-y = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.842 |
|
|
\[
{}x y^{\prime }-x \left (y-x \right ) \sqrt {x^{2}+y^{2}}-y = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
5.893 |
|
|
\[
{}x y^{\prime }-x \,{\mathrm e}^{\frac {y}{x}}-y-x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.996 |
|
|
\[
{}x y^{\prime }-y \ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
1.953 |
|
|
\[
{}x y^{\prime }-y \left (\ln \left (x y\right )-1\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.936 |
|
|
\[
{}x y^{\prime }-y \left (x \ln \left (\frac {x^{2}}{y}\right )+2\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.787 |
|
|
\[
{}x y^{\prime }-\sin \left (x -y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.755 |
|
|
\[
{}x y^{\prime }+\left (\sin \left (y\right )-3 x^{2} \cos \left (y\right )\right ) \cos \left (y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.665 |
|
|
\[
{}x y^{\prime }-x \sin \left (\frac {y}{x}\right )-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.579 |
|
|
\[
{}x y^{\prime }+x \cos \left (\frac {y}{x}\right )-y+x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.443 |
|
|
\[
{}x y^{\prime }+x \tan \left (\frac {y}{x}\right )-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.863 |
|
|
\[
{}x y^{\prime }-y f \left (x y\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.900 |
|
|
\[
{}x y^{\prime }-y f \left (x^{a} y^{b}\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.524 |
|
|
\[
{}x y^{\prime }+a y-f \left (x \right ) g \left (x^{a} y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.291 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y \left (y-x \right ) = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.318 |
|
|
\[
{}2 x y^{\prime }-y-2 x^{3} = 0
\] |
[_linear] |
✓ |
2.078 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2 = 0
\] |
[_separable] |
✓ |
2.383 |
|
|
\[
{}3 x y^{\prime }-3 x \ln \left (x \right ) y^{4}-y = 0
\] |
[_Bernoulli] |
✓ |
3.319 |
|
|
\[
{}x^{2} y^{\prime }+y-x = 0
\] |
[_linear] |
✓ |
1.186 |
|
|
\[
{}x^{2} y^{\prime }-y+x^{2} {\mathrm e}^{x -\frac {1}{x}} = 0
\] |
[_linear] |
✓ |
1.617 |
|
|
\[
{}x^{2} y^{\prime }-\left (-1+x \right ) y = 0
\] |
[_separable] |
✓ |
1.782 |
|
|
\[
{}x^{2} y^{\prime }+y^{2}+x y+x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.214 |
|
|
\[
{}x^{2} y^{\prime }-y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.388 |
|
|
\[
{}x^{2} y^{\prime }-y^{2}-x y-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.470 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )+a \,x^{k}-b \left (b -1\right ) = 0
\] |
[_rational, _Riccati] |
✓ |
2.484 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )+4 x y+2 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.901 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )+y a x +b = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.533 |
|
|
\[
{}x^{2} \left (y^{\prime }-y^{2}\right )-y a \,x^{2}+a x +2 = 0
\] |
[_rational, _Riccati] |
✓ |
1.829 |
|
|
\[
{}x^{2} \left (y^{\prime }+a y^{2}\right )-b = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
1.401 |
|
|
\[
{}x^{2} \left (y^{\prime }+a y^{2}\right )+b \,x^{\alpha }+c = 0
\] |
[_rational, _Riccati] |
✓ |
2.494 |
|
|
\[
{}x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.925 |
|
|
\[
{}x^{2} y^{\prime }+x y^{3}+a y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.928 |
|
|
\[
{}x^{2} y^{\prime }+a \,x^{2} y^{3}+b y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
1.034 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y-1 = 0
\] |
[_linear] |
✓ |
1.288 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y-x \left (x^{2}+1\right ) = 0
\] |
[_linear] |
✓ |
3.681 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y-2 x^{2} = 0
\] |
[_linear] |
✓ |
1.312 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 x y-1\right ) = 0
\] |
[_rational, _Abel] |
✗ |
1.329 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )-x \left (x^{2}+1\right ) \cos \left (y\right )^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
18.305 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-x y+a = 0
\] |
[_linear] |
✓ |
1.980 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.796 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 x y+1 = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
1.920 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-y \left (y-x \right ) = 0
\] |
[_rational, _Bernoulli] |
✓ |
2.825 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+a \left (y^{2}-2 x y+1\right ) = 0
\] |
[_rational, _Riccati] |
✗ |
7.806 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+a x y^{2}+x y = 0
\] |
[_separable] |
✓ |
2.280 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
2.492 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y^{2}-4 y = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.593 |
|
|
\[
{}\left (x^{2}-5 x +6\right ) y^{\prime }+3 x y-8 y+x^{2} = 0
\] |
[_linear] |
✓ |
1.638 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+y^{2}+k \left (y+x -a \right ) \left (y+x -b \right ) = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
3.374 |
|
|
\[
{}2 x^{2} y^{\prime }-2 y^{2}-x y+2 a^{2} x = 0
\] |
[_rational, _Riccati] |
✓ |
1.386 |
|
|
\[
{}2 x^{2} y^{\prime }-2 y^{2}-3 x y+2 a^{2} x = 0
\] |
[_rational, _Riccati] |
✓ |
1.882 |
|
|
\[
{}x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (1+4 x \right ) y+4 x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.789 |
|
|
\[
{}2 x \left (-1+x \right ) y^{\prime }+\left (-1+x \right ) y^{2}-x = 0
\] |
[_rational, _Riccati] |
✓ |
2.464 |
|
|
\[
{}3 x^{2} y^{\prime }-7 y^{2}-3 x y-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.828 |
|
|
\[
{}3 \left (x^{2}-4\right ) y^{\prime }+y^{2}-x y-3 = 0
\] |
[_rational, _Riccati] |
✓ |
151.636 |
|
|
\[
{}\left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
2.324 |
|
|
\[
{}x^{3} y^{\prime }-y^{2}-x^{4} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.408 |
|
|
\[
{}x^{3} y^{\prime }-y^{2}-x^{2} y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.289 |
|
|
\[
{}x^{3} y^{\prime }-x^{4} y^{2}+x^{2} y+20 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
2.035 |
|
|
\[
{}x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3 = 0
\] |
[_rational, _Riccati] |
✓ |
1.599 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime }+x^{2} y = 0
\] |
[_separable] |
✓ |
1.658 |
|
|
\[
{}x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3} = 0
\] |
[_linear] |
✓ |
1.162 |
|
|
\[
{}x \left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right ) y^{2}-x^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
135.729 |
|
|
\[
{}x^{2} \left (-1+x \right ) y^{\prime }-y^{2}-x \left (-2+x \right ) y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.466 |
|
|
\[
{}2 x \left (x^{2}-1\right ) y^{\prime }+2 \left (x^{2}-1\right ) y^{2}-\left (3 x^{2}-5\right ) y+x^{2}-3 = 0
\] |
[_rational, _Riccati] |
✓ |
2.182 |
|
|
\[
{}3 x \left (x^{2}-1\right ) y^{\prime }+x y^{2}-\left (x^{2}+1\right ) y-3 x = 0
\] |
[_rational, _Riccati] |
✓ |
42.022 |
|
|
\[
{}\left (a \,x^{2}+b x +c \right ) \left (-y+x y^{\prime }\right )-y^{2}+x^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.112 |
|
|
\[
{}x^{4} \left (y^{\prime }+y^{2}\right )+a = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
1.263 |
|
|
\[
{}x \left (x^{3}-1\right ) y^{\prime }-2 x y^{2}+y+x^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
2.030 |
|
|
\[
{}\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y = 0
\] |
[_separable] |
✓ |
1.828 |
|
|
\[
{}\left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\] |
[_rational, _Riccati] |
✓ |
3.539 |
|
|
\[
{}x^{7} y^{\prime }+2 \left (x^{2}+1\right ) y^{3}+5 x^{3} y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
1.143 |
|
|
\[
{}x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{-2+2 n} = 0
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
2.092 |
|
|
\[
{}x^{n} y^{\prime }-a y^{2}-b \,x^{-2+2 n} = 0
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
4.001 |
|
|
\[
{}x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n} = 0
\] |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
4.309 |
|
|
\[
{}x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (m +1\right )} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.734 |
|