|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{\prime }+y^{3}+3 x y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.833 |
|
|
\[
{}x y^{\prime }-\sqrt {y^{2}+x^{2}}-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.522 |
|
|
\[
{}x y^{\prime }+a \sqrt {y^{2}+x^{2}}-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
11.084 |
|
|
\[
{}x y^{\prime }-x \sqrt {y^{2}+x^{2}}-y = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.964 |
|
|
\[
{}x y^{\prime }-x \left (y-x \right ) \sqrt {y^{2}+x^{2}}-y = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
5.346 |
|
|
\[
{}x y^{\prime }-x \,{\mathrm e}^{\frac {y}{x}}-y-x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.428 |
|
|
\[
{}x y^{\prime }-y \ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
1.618 |
|
|
\[
{}x y^{\prime }-y \left (\ln \left (x y\right )-1\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.749 |
|
|
\[
{}x y^{\prime }-y \left (x \ln \left (\frac {x^{2}}{y}\right )+2\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.562 |
|
|
\[
{}x y^{\prime }-\sin \left (x -y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.688 |
|
|
\[
{}x y^{\prime }+\left (\sin \left (y\right )-3 x^{2} \cos \left (y\right )\right ) \cos \left (y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.467 |
|
|
\[
{}x y^{\prime }-x \sin \left (\frac {y}{x}\right )-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.353 |
|
|
\[
{}x y^{\prime }+x \cos \left (\frac {y}{x}\right )-y+x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.910 |
|
|
\[
{}x y^{\prime }+x \tan \left (\frac {y}{x}\right )-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.430 |
|
|
\[
{}x y^{\prime }-y f \left (x y\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.934 |
|
|
\[
{}x y^{\prime }-y f \left (x^{a} y^{b}\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.270 |
|
|
\[
{}x y^{\prime }+a y-f \left (x \right ) g \left (x^{a} y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.110 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+\left (y-x \right ) y = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.132 |
|
|
\[
{}2 x y^{\prime }-y-2 x^{3} = 0
\] |
[_linear] |
✓ |
1.832 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2 = 0
\] |
[_separable] |
✓ |
1.599 |
|
|
\[
{}3 x y^{\prime }-3 x \ln \left (x \right ) y^{4}-y = 0
\] |
[_Bernoulli] |
✓ |
3.076 |
|
|
\[
{}x^{2} y^{\prime }+y-x = 0
\] |
[_linear] |
✓ |
0.993 |
|
|
\[
{}x^{2} y^{\prime }-y+x^{2} {\mathrm e}^{x -\frac {1}{x}} = 0
\] |
[_linear] |
✓ |
1.342 |
|
|
\[
{}x^{2} y^{\prime }-\left (x -1\right ) y = 0
\] |
[_separable] |
✓ |
1.384 |
|
|
\[
{}x^{2} y^{\prime }+y^{2}+x y+x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.758 |
|
|
\[
{}x^{2} y^{\prime }-y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.800 |
|
|
\[
{}x^{2} y^{\prime }-y^{2}-x y-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.191 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )+a \,x^{k}-b \left (b -1\right ) = 0
\] |
[_rational, _Riccati] |
✓ |
2.105 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )+4 x y+2 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.658 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.566 |
|
|
\[
{}x^{2} \left (y^{\prime }-y^{2}\right )-a \,x^{2} y+a x +2 = 0
\] |
[_rational, _Riccati] |
✓ |
1.676 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2} a \right )-b = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
1.475 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2} a \right )+b \,x^{\alpha }+c = 0
\] |
[_rational, _Riccati] |
✓ |
2.296 |
|
|
\[
{}x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.902 |
|
|
\[
{}x^{2} y^{\prime }+x y^{3}+y^{2} a = 0
\] |
[_rational, _Abel] |
✗ |
0.924 |
|
|
\[
{}x^{2} y^{\prime }+a \,x^{2} y^{3}+b y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.983 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y-1 = 0
\] |
[_linear] |
✓ |
1.107 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y-x \left (x^{2}+1\right ) = 0
\] |
[_linear] |
✓ |
3.237 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y-2 x^{2} = 0
\] |
[_linear] |
✓ |
1.087 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 x y-1\right ) = 0
\] |
[_rational, _Abel] |
✗ |
1.303 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )-x \left (x^{2}+1\right ) \cos \left (y\right )^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
15.073 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-x y+a = 0
\] |
[_linear] |
✓ |
2.082 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.432 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 x y+1 = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
1.670 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-\left (y-x \right ) y = 0
\] |
[_rational, _Bernoulli] |
✓ |
2.405 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+a \left (y^{2}-2 x y+1\right ) = 0
\] |
[_rational, _Riccati] |
✗ |
6.478 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+a x y^{2}+x y = 0
\] |
[_separable] |
✓ |
2.129 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
2.517 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y^{2}-4 y = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.401 |
|
|
\[
{}\left (x^{2}-5 x +6\right ) y^{\prime }+3 x y-8 y+x^{2} = 0
\] |
[_linear] |
✓ |
1.464 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+y^{2}+k \left (y+x -a \right ) \left (y+x -b \right ) = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.909 |
|
|
\[
{}2 x^{2} y^{\prime }-2 y^{2}-x y+2 a^{2} x = 0
\] |
[_rational, _Riccati] |
✓ |
1.494 |
|
|
\[
{}2 x^{2} y^{\prime }-2 y^{2}-3 x y+2 a^{2} x = 0
\] |
[_rational, _Riccati] |
✓ |
1.692 |
|
|
\[
{}x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (1+4 x \right ) y+4 x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.354 |
|
|
\[
{}2 x \left (x -1\right ) y^{\prime }+\left (x -1\right ) y^{2}-x = 0
\] |
[_rational, _Riccati] |
✓ |
2.170 |
|
|
\[
{}3 x^{2} y^{\prime }-7 y^{2}-3 x y-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.477 |
|
|
\[
{}3 \left (x^{2}-4\right ) y^{\prime }+y^{2}-x y-3 = 0
\] |
[_rational, _Riccati] |
✓ |
150.731 |
|
|
\[
{}\left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
1.949 |
|
|
\[
{}x^{3} y^{\prime }-y^{2}-x^{4} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.176 |
|
|
\[
{}x^{3} y^{\prime }-y^{2}-x^{2} y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.742 |
|
|
\[
{}x^{3} y^{\prime }-x^{4} y^{2}+x^{2} y+20 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.888 |
|
|
\[
{}x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3 = 0
\] |
[_rational, _Riccati] |
✓ |
1.757 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime }+x^{2} y = 0
\] |
[_separable] |
✓ |
1.314 |
|
|
\[
{}x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3} = 0
\] |
[_linear] |
✓ |
1.142 |
|
|
\[
{}x \left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right ) y^{2}-x^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
106.964 |
|
|
\[
{}x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (-2+x \right ) y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.039 |
|
|
\[
{}2 x \left (x^{2}-1\right ) y^{\prime }+2 \left (x^{2}-1\right ) y^{2}-\left (3 x^{2}-5\right ) y+x^{2}-3 = 0
\] |
[_rational, _Riccati] |
✓ |
1.961 |
|
|
\[
{}3 x \left (x^{2}-1\right ) y^{\prime }+x y^{2}-\left (x^{2}+1\right ) y-3 x = 0
\] |
[_rational, _Riccati] |
✓ |
45.882 |
|
|
\[
{}\left (x^{2} a +b x +c \right ) \left (-y+x y^{\prime }\right )-y^{2}+x^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.743 |
|
|
\[
{}x^{4} \left (y^{\prime }+y^{2}\right )+a = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
1.307 |
|
|
\[
{}x \left (x^{3}-1\right ) y^{\prime }-2 x y^{2}+y+x^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
1.699 |
|
|
\[
{}\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y = 0
\] |
[_separable] |
✓ |
1.510 |
|
|
\[
{}\left (x^{2} a +b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\] |
[_rational, _Riccati] |
✓ |
3.727 |
|
|
\[
{}x^{7} y^{\prime }+2 \left (x^{2}+1\right ) y^{3}+5 x^{3} y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
1.246 |
|
|
\[
{}x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{-2+2 n} = 0
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
2.281 |
|
|
\[
{}x^{n} y^{\prime }-y^{2} a -b \,x^{-2+2 n} = 0
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
3.932 |
|
|
\[
{}x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n} = 0
\] |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
7.609 |
|
|
\[
{}x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (m +1\right )} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.538 |
|
|
\[
{}\sqrt {x^{2}-1}\, y^{\prime }-\sqrt {y^{2}-1} = 0
\] |
[_separable] |
✓ |
8.359 |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{\prime }-y \sqrt {y^{2}-1} = 0
\] |
[_separable] |
✓ |
10.082 |
|
|
\[
{}\sqrt {a^{2}+x^{2}}\, y^{\prime }+y-\sqrt {a^{2}+x^{2}}+x = 0
\] |
[_linear] |
✓ |
1.524 |
|
|
\[
{}x y^{\prime } \ln \left (x \right )+y-a x \left (\ln \left (x \right )+1\right ) = 0
\] |
[_linear] |
✓ |
1.311 |
|
|
\[
{}x y^{\prime } \ln \left (x \right )-y^{2} \ln \left (x \right )-\left (2 \ln \left (x \right )^{2}+1\right ) y-\ln \left (x \right )^{3} = 0
\] |
[_Riccati] |
✓ |
2.434 |
|
|
\[
{}\sin \left (x \right ) y^{\prime }-y^{2} \sin \left (x \right )^{2}+\left (\cos \left (x \right )-3 \sin \left (x \right )\right ) y+4 = 0
\] |
[_Riccati] |
✓ |
9.084 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }+y+\left (\sin \left (x \right )+1\right ) \cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.701 |
|
|
\[
{}\cos \left (x \right ) y^{\prime }-y^{4}-y \sin \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
6.188 |
|
|
\[
{}\sin \left (x \right ) \cos \left (x \right ) y^{\prime }-y-\sin \left (x \right )^{3} = 0
\] |
[_linear] |
✓ |
3.875 |
|
|
\[
{}\sin \left (2 x \right ) y^{\prime }+\sin \left (2 y\right ) = 0
\] |
[_separable] |
✓ |
20.085 |
|
|
\[
{}\left (a \sin \left (x \right )^{2}+b \right ) y^{\prime }+a y \sin \left (2 x \right )+A x \left (a \sin \left (x \right )^{2}+c \right ) = 0
\] |
[_linear] |
✓ |
13.364 |
|
|
\[
{}2 f \left (x \right ) y^{\prime }+2 f \left (x \right ) y^{2}-f^{\prime }\left (x \right ) y-2 f \left (x \right )^{2} = 0
\] |
[_Riccati] |
✓ |
1.035 |
|
|
\[
{}f \left (x \right ) y^{\prime }+g \left (x \right ) s \left (y\right )+h \left (x \right ) = 0
\] |
[NONE] |
✗ |
1.260 |
|
|
\[
{}y y^{\prime }+y+x^{3} = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.659 |
|
|
\[
{}y y^{\prime }+a y+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
9.513 |
|
|
\[
{}y y^{\prime }+a y+\frac {\left (a^{2}-1\right ) x}{4}+b \,x^{n} = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.049 |
|
|
\[
{}y y^{\prime }+a y+b \,{\mathrm e}^{x}-2 a = 0
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.402 |
|
|
\[
{}y y^{\prime }+y^{2}+4 x \left (x +1\right ) = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.829 |
|
|
\[
{}y y^{\prime }+y^{2} a -b \cos \left (x +c \right ) = 0
\] |
[_Bernoulli] |
✓ |
2.809 |
|
|
\[
{}y y^{\prime }-\sqrt {y^{2} a +b} = 0
\] |
[_quadrature] |
✓ |
8.276 |
|
|
\[
{}y y^{\prime }+x y^{2}-4 x = 0
\] |
[_separable] |
✓ |
1.706 |
|
|
\[
{}y y^{\prime }-x \,{\mathrm e}^{\frac {x}{y}} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.276 |
|