|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }-\frac {y a f \left (x^{c} y\right )+c \,x^{a} y^{b}}{x b f \left (x^{c} y\right )-x^{a} y^{b}} = 0
\] |
[NONE] |
✗ |
5.258 |
|
|
\[
{}2 y^{\prime }-3 y^{2}-4 a y-b -c \,{\mathrm e}^{-2 a x} = 0
\] |
[_Riccati] |
✓ |
2.138 |
|
|
\[
{}y^{\prime } x -\sqrt {a^{2}-x^{2}} = 0
\] |
[_quadrature] |
✓ |
0.536 |
|
|
\[
{}y^{\prime } x +y-x \sin \left (x \right ) = 0
\] |
[_linear] |
✓ |
1.346 |
|
|
\[
{}y^{\prime } x -y-\frac {x}{\ln \left (x \right )} = 0
\] |
[_linear] |
✓ |
1.336 |
|
|
\[
{}y^{\prime } x -y-x^{2} \sin \left (x \right ) = 0
\] |
[_linear] |
✓ |
1.561 |
|
|
\[
{}y^{\prime } x -y-\frac {x \cos \left (\ln \left (\ln \left (x \right )\right )\right )}{\ln \left (x \right )} = 0
\] |
[_linear] |
✓ |
2.260 |
|
|
\[
{}y^{\prime } x +a y+b \,x^{n} = 0
\] |
[_linear] |
✓ |
1.057 |
|
|
\[
{}y^{\prime } x +y^{2}+x^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
1.126 |
|
|
\[
{}y^{\prime } x -y^{2}+1 = 0
\] |
[_separable] |
✓ |
1.862 |
|
|
\[
{}y^{\prime } x +a y^{2}-y+b \,x^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.395 |
|
|
\[
{}y^{\prime } x +a y^{2}-b y+c \,x^{2 b} = 0
\] |
[_rational, _Riccati] |
✓ |
2.827 |
|
|
\[
{}y^{\prime } x +a y^{2}-b y-c \,x^{\beta } = 0
\] |
[_rational, _Riccati] |
✓ |
2.115 |
|
|
\[
{}y^{\prime } x +x y^{2}+a = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
0.997 |
|
|
\[
{}y^{\prime } x +x y^{2}-y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.153 |
|
|
\[
{}y^{\prime } x +x y^{2}-y-a \,x^{3} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.810 |
|
|
\[
{}y^{\prime } x +x y^{2}-\left (2 x^{2}+1\right ) y-x^{3} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
3.239 |
|
|
\[
{}y^{\prime } x +a x y^{2}+2 y+b x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.447 |
|
|
\[
{}y^{\prime } x +a x y^{2}+b y+c x +d = 0
\] |
[_rational, _Riccati] |
✓ |
7.266 |
|
|
\[
{}y^{\prime } x +x^{a} y^{2}+\frac {\left (a -b \right ) y}{2}+x^{b} = 0
\] |
[_rational, _Riccati] |
✓ |
2.282 |
|
|
\[
{}y^{\prime } x +a \,x^{\alpha } y^{2}+b y-c \,x^{\beta } = 0
\] |
[_rational, _Riccati] |
✓ |
3.178 |
|
|
\[
{}y^{\prime } x -y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
2.108 |
|
|
\[
{}y^{\prime } x -y \left (2 y \ln \left (x \right )-1\right ) = 0
\] |
[_Bernoulli] |
✓ |
2.184 |
|
|
\[
{}y^{\prime } x +f \left (x \right ) \left (y^{2}-x^{2}\right )-y = 0
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
2.234 |
|
|
\[
{}y^{\prime } x +y^{3}+3 x y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.803 |
|
|
\[
{}y^{\prime } x -\sqrt {x^{2}+y^{2}}-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.664 |
|
|
\[
{}y^{\prime } x +a \sqrt {x^{2}+y^{2}}-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
11.083 |
|
|
\[
{}y^{\prime } x -x \sqrt {x^{2}+y^{2}}-y = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.981 |
|
|
\[
{}y^{\prime } x -x \left (y-x \right ) \sqrt {x^{2}+y^{2}}-y = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
5.110 |
|
|
\[
{}y^{\prime } x -x \,{\mathrm e}^{\frac {y}{x}}-y-x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.605 |
|
|
\[
{}y^{\prime } x -y \ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
1.840 |
|
|
\[
{}y^{\prime } x -y \left (\ln \left (x y\right )-1\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.893 |
|
|
\[
{}y^{\prime } x -y \left (x \ln \left (\frac {x^{2}}{y}\right )+2\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.354 |
|
|
\[
{}y^{\prime } x -\sin \left (x -y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.807 |
|
|
\[
{}y^{\prime } x +\left (\sin \left (y\right )-3 x^{2} \cos \left (y\right )\right ) \cos \left (y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.622 |
|
|
\[
{}y^{\prime } x -x \sin \left (\frac {y}{x}\right )-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.846 |
|
|
\[
{}y^{\prime } x +x \cos \left (\frac {y}{x}\right )-y+x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.402 |
|
|
\[
{}y^{\prime } x +x \tan \left (\frac {y}{x}\right )-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.109 |
|
|
\[
{}y^{\prime } x -y f \left (x y\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.965 |
|
|
\[
{}y^{\prime } x -y f \left (x^{a} y^{b}\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.332 |
|
|
\[
{}y^{\prime } x +a y-f \left (x \right ) g \left (x^{a} y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
2.774 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y \left (y-x \right ) = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.249 |
|
|
\[
{}2 y^{\prime } x -y-2 x^{3} = 0
\] |
[_linear] |
✓ |
2.247 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2 = 0
\] |
[_separable] |
✓ |
1.890 |
|
|
\[
{}3 y^{\prime } x -3 x \ln \left (x \right ) y^{4}-y = 0
\] |
[_Bernoulli] |
✓ |
3.161 |
|
|
\[
{}x^{2} y^{\prime }+y-x = 0
\] |
[_linear] |
✓ |
1.170 |
|
|
\[
{}x^{2} y^{\prime }-y+x^{2} {\mathrm e}^{x -\frac {1}{x}} = 0
\] |
[_linear] |
✓ |
1.530 |
|
|
\[
{}x^{2} y^{\prime }-\left (x -1\right ) y = 0
\] |
[_separable] |
✓ |
1.762 |
|
|
\[
{}x^{2} y^{\prime }+y^{2}+x y+x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.239 |
|
|
\[
{}x^{2} y^{\prime }-y^{2}-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.375 |
|
|
\[
{}x^{2} y^{\prime }-y^{2}-x y-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.615 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )+a \,x^{k}-b \left (b -1\right ) = 0
\] |
[_rational, _Riccati] |
✓ |
2.144 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )+4 x y+2 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.980 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )+y a x +b = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.552 |
|
|
\[
{}x^{2} \left (y^{\prime }-y^{2}\right )-y a \,x^{2}+a x +2 = 0
\] |
[_rational, _Riccati] |
✓ |
1.740 |
|
|
\[
{}x^{2} \left (y^{\prime }+a y^{2}\right )-b = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
1.549 |
|
|
\[
{}x^{2} \left (y^{\prime }+a y^{2}\right )+b \,x^{\alpha }+c = 0
\] |
[_rational, _Riccati] |
✓ |
2.377 |
|
|
\[
{}x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.850 |
|
|
\[
{}x^{2} y^{\prime }+x y^{3}+a y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.869 |
|
|
\[
{}x^{2} y^{\prime }+a \,x^{2} y^{3}+b y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.949 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y-1 = 0
\] |
[_linear] |
✓ |
1.276 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y-x \left (x^{2}+1\right ) = 0
\] |
[_linear] |
✓ |
3.606 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 x y-2 x^{2} = 0
\] |
[_linear] |
✓ |
1.308 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 x y-1\right ) = 0
\] |
[_rational, _Abel] |
✗ |
1.228 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )-x \left (x^{2}+1\right ) \cos \left (y\right )^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
14.951 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-x y+a = 0
\] |
[_linear] |
✓ |
2.201 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 x y-\cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.835 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 x y+1 = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
1.856 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-y \left (y-x \right ) = 0
\] |
[_rational, _Bernoulli] |
✓ |
2.615 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+a \left (y^{2}-2 x y+1\right ) = 0
\] |
[_rational, _Riccati] |
✗ |
6.198 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+a x y^{2}+x y = 0
\] |
[_separable] |
✓ |
2.227 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
2.425 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y^{2}-4 y = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.573 |
|
|
\[
{}\left (x^{2}-5 x +6\right ) y^{\prime }+3 x y-8 y+x^{2} = 0
\] |
[_linear] |
✓ |
1.665 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+y^{2}+k \left (y+x -a \right ) \left (y+x -b \right ) = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
3.140 |
|
|
\[
{}2 x^{2} y^{\prime }-2 y^{2}-x y+2 a^{2} x = 0
\] |
[_rational, _Riccati] |
✓ |
1.529 |
|
|
\[
{}2 x^{2} y^{\prime }-2 y^{2}-3 x y+2 a^{2} x = 0
\] |
[_rational, _Riccati] |
✓ |
1.865 |
|
|
\[
{}x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (1+4 x \right ) y+4 x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.592 |
|
|
\[
{}2 x \left (x -1\right ) y^{\prime }+\left (x -1\right ) y^{2}-x = 0
\] |
[_rational, _Riccati] |
✓ |
2.283 |
|
|
\[
{}3 x^{2} y^{\prime }-7 y^{2}-3 x y-x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.963 |
|
|
\[
{}3 \left (x^{2}-4\right ) y^{\prime }+y^{2}-x y-3 = 0
\] |
[_rational, _Riccati] |
✓ |
154.087 |
|
|
\[
{}\left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
1.852 |
|
|
\[
{}x^{3} y^{\prime }-y^{2}-x^{4} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.487 |
|
|
\[
{}x^{3} y^{\prime }-y^{2}-x^{2} y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.247 |
|
|
\[
{}x^{3} y^{\prime }-y^{2} x^{4}+x^{2} y+20 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
2.188 |
|
|
\[
{}x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3 = 0
\] |
[_rational, _Riccati] |
✓ |
1.933 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime }+x^{2} y = 0
\] |
[_separable] |
✓ |
1.980 |
|
|
\[
{}x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3} = 0
\] |
[_linear] |
✓ |
1.305 |
|
|
\[
{}x \left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right ) y^{2}-x^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
110.098 |
|
|
\[
{}x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.286 |
|
|
\[
{}2 x \left (x^{2}-1\right ) y^{\prime }+2 \left (x^{2}-1\right ) y^{2}-\left (3 x^{2}-5\right ) y+x^{2}-3 = 0
\] |
[_rational, _Riccati] |
✓ |
2.134 |
|
|
\[
{}3 x \left (x^{2}-1\right ) y^{\prime }+x y^{2}-\left (x^{2}+1\right ) y-3 x = 0
\] |
[_rational, _Riccati] |
✓ |
64.026 |
|
|
\[
{}\left (a \,x^{2}+b x +c \right ) \left (-y+y^{\prime } x \right )-y^{2}+x^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.773 |
|
|
\[
{}x^{4} \left (y^{\prime }+y^{2}\right )+a = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
1.378 |
|
|
\[
{}x \left (x^{3}-1\right ) y^{\prime }-2 x y^{2}+y+x^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
1.819 |
|
|
\[
{}\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y = 0
\] |
[_separable] |
✓ |
1.964 |
|
|
\[
{}\left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\] |
[_rational, _Riccati] |
✓ |
3.936 |
|
|
\[
{}x^{7} y^{\prime }+2 \left (x^{2}+1\right ) y^{3}+5 x^{3} y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
1.132 |
|
|
\[
{}x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{2 n -2} = 0
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
2.358 |
|
|
\[
{}x^{n} y^{\prime }-a y^{2}-b \,x^{2 n -2} = 0
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
4.273 |
|