|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {y^{3} {\mathrm e}^{-2 x}}{y \,{\mathrm e}^{-x}+1}
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.533 |
|
|
\[
{}y^{\prime } = \frac {\left (-2 y^{{3}/{2}}+3 \,{\mathrm e}^{x}\right )^{2} {\mathrm e}^{x}}{4 \sqrt {y}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.708 |
|
|
\[
{}y^{\prime } = \frac {i x \left (i-2 \sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y\right )}\right ) y}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
5.348 |
|
|
\[
{}y^{\prime } = \frac {\left (x y^{2}+1\right )^{2}}{y x^{4}}
\] |
[_rational] |
✗ |
1.425 |
|
|
\[
{}y^{\prime } = \frac {x^{2} \left (3 x +\sqrt {-9 x^{4}+4 y^{3}}\right )}{y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
5.070 |
|
|
\[
{}y^{\prime } = \frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{2}+x^{2}}{2 x}
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.462 |
|
|
\[
{}y^{\prime } = -\frac {x^{2}-x -2-2 \sqrt {x^{2}-4 x +4 y}}{2 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.519 |
|
|
\[
{}y^{\prime } = \frac {y+x^{3} a \,{\mathrm e}^{x}+a \,x^{4}+a \,x^{3}-x y^{2} {\mathrm e}^{x}-x^{2} y^{2}-x y^{2}}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
2.676 |
|
|
\[
{}y^{\prime } = \frac {x +1+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3} \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.968 |
|
|
\[
{}y^{\prime } = \frac {y+x^{3} a \ln \left (x +1\right )+a \,x^{4}+a \,x^{3}-x y^{2} \ln \left (x +1\right )-x^{2} y^{2}-x y^{2}}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
3.164 |
|
|
\[
{}y^{\prime } = \frac {x^{2} \left (x +1+2 x \sqrt {x^{3}-6 y}\right )}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
1.933 |
|
|
\[
{}y^{\prime } = \frac {y+x^{3} \ln \left (x \right )+x^{4}+x^{3}+7 x y^{2} \ln \left (x \right )+7 x^{2} y^{2}+7 x y^{2}}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
6.089 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+2 x +1+2 \sqrt {x^{2}+2 x +1-4 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.573 |
|
|
\[
{}y^{\prime } = \frac {y+x^{3} b \ln \left (\frac {1}{x}\right )+x^{4} b +b \,x^{3}+x a y^{2} \ln \left (\frac {1}{x}\right )+a \,x^{2} y^{2}+a x y^{2}}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
6.184 |
|
|
\[
{}y^{\prime } = \frac {2 a}{x \left (-y x +2 a x y^{2}-8 a^{2}\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.347 |
|
|
\[
{}y^{\prime } = \frac {y \left (-1+\ln \left (x \left (x +1\right )\right ) y x^{4}-\ln \left (x \left (x +1\right )\right ) x^{3}\right )}{x}
\] |
[_Bernoulli] |
✓ |
7.170 |
|
|
\[
{}y^{\prime } = \frac {y+\sqrt {x^{2}+y^{2}}\, x^{2}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.443 |
|
|
\[
{}y^{\prime } = \frac {y+\ln \left (\left (x +1\right ) \left (x -1\right )\right ) x^{3}+7 \ln \left (\left (x +1\right ) \left (x -1\right )\right ) x y^{2}}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
3.446 |
|
|
\[
{}y^{\prime } = \frac {y^{3} x \,{\mathrm e}^{2 x^{2}}}{y \,{\mathrm e}^{x^{2}}+1}
\] |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.674 |
|
|
\[
{}y^{\prime } = \frac {y-\ln \left (\frac {x +1}{x -1}\right ) x^{3}+\ln \left (\frac {x +1}{x -1}\right ) x y^{2}}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
3.563 |
|
|
\[
{}y^{\prime } = \frac {y+{\mathrm e}^{\frac {x +1}{x -1}} x^{3}+{\mathrm e}^{\frac {x +1}{x -1}} x y^{2}}{x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
3.242 |
|
|
\[
{}y^{\prime } = \frac {y x -y-{\mathrm e}^{x +1} x^{3}+{\mathrm e}^{x +1} x y^{2}}{\left (x -1\right ) x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
2.382 |
|
|
\[
{}y^{\prime } = \frac {-x^{2}+1+4 x^{3} \sqrt {x^{2}-2 x +1+8 y}}{4 x +4}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
1.965 |
|
|
\[
{}y^{\prime } = \frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{3}+x^{3}}{2 x}
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.585 |
|
|
\[
{}y^{\prime } = \frac {y+x^{3} \sqrt {x^{2}+y^{2}}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.581 |
|
|
\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-2 b x}+y^{3} {\mathrm e}^{-3 b x}\right ) {\mathrm e}^{b x}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
1.608 |
|
|
\[
{}y^{\prime } = \frac {x +1+2 \sqrt {4 x^{2} y+1}\, x^{3}}{2 x^{3} \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.991 |
|
|
\[
{}y^{\prime } = \frac {y \ln \left (x -1\right )+x^{4}+x^{3}+x^{2} y^{2}+x y^{2}}{\ln \left (x -1\right ) x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
3.195 |
|
|
\[
{}y^{\prime } = \frac {y \ln \left (x -1\right )+{\mathrm e}^{x +1} x^{3}+7 \,{\mathrm e}^{x +1} x y^{2}}{\ln \left (x -1\right ) x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
3.511 |
|
|
\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+y^{3} {\mathrm e}^{-2 x}\right ) {\mathrm e}^{\frac {2 x}{3}}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
2.142 |
|
|
\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-2 x}+y^{3} {\mathrm e}^{-3 x}\right ) {\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
1.594 |
|
|
\[
{}y^{\prime } = \frac {x \left (-2 x -2+3 x^{2} \sqrt {x^{2}+3 y}\right )}{3 x +3}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
1.904 |
|
|
\[
{}y^{\prime } = \frac {1}{x \left (x y^{2}+1+x \right ) y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✗ |
1.069 |
|
|
\[
{}y^{\prime } = \frac {2 x \,{\mathrm e}^{x}-2 x -\ln \left (x \right )-1+x^{4} \ln \left (x \right )+x^{4}-2 y x^{2} \ln \left (x \right )-2 x^{2} y+y^{2} \ln \left (x \right )+y^{2}}{{\mathrm e}^{x}-1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
13.847 |
|
|
\[
{}y^{\prime } = \frac {-y \,{\mathrm e}^{x}+y x -x^{3} \ln \left (x \right )-x^{3}-x y^{2} \ln \left (x \right )-x y^{2}}{\left (-{\mathrm e}^{x}+x \right ) x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
3.601 |
|
|
\[
{}y^{\prime } = \frac {y \left (1-x +y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (x -1\right ) x}
\] |
[_Bernoulli] |
✓ |
4.241 |
|
|
\[
{}y^{\prime } = \frac {y \ln \left (x \right ) x -y+2 x^{5} b +2 x^{3} a y^{2}}{\left (x \ln \left (x \right )-1\right ) x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
3.672 |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right )+x +x^{3}+x^{4}\right ) y}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.971 |
|
|
\[
{}y^{\prime } = -\frac {\left (-\ln \left (-1+y\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right ) x \left (1+y\right )^{2}}{8}
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.885 |
|
|
\[
{}y^{\prime } = \frac {\left (-\ln \left (-1+y\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right )^{2} x \left (1+y\right )^{2}}{16}
\] |
[‘y=_G(x,y’)‘] |
✗ |
5.158 |
|
|
\[
{}y^{\prime } = \frac {\left (-y^{2}+4 a x \right )^{3}}{\left (-y^{2}+4 a x -1\right ) y}
\] |
[_rational] |
✗ |
1.464 |
|
|
\[
{}y^{\prime } = \frac {2 a x +2 a +x^{3} \sqrt {-y^{2}+4 a x}}{\left (x +1\right ) y}
\] |
[‘y=_G(x,y’)‘] |
✗ |
74.682 |
|
|
\[
{}y^{\prime } = \frac {-\ln \left (x \right )+{\mathrm e}^{\frac {1}{x}}+4 x^{2} y+2 x +2 x y^{2}+2 x^{3}}{\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
215.110 |
|
|
\[
{}y^{\prime } = -\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-1\right ) y}{x +1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.674 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+2 x +1+2 x^{3} \sqrt {x^{2}+2 x +1-4 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
1.974 |
|
|
\[
{}y^{\prime } = \frac {-b y a +b^{2}+a b +b^{2} x -b a \sqrt {x}-a^{2}}{a \left (-a y+b +a +b x -a \sqrt {x}\right )}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.385 |
|
|
\[
{}y^{\prime } = -\frac {y \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}+y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right ) x}
\] |
[_Bernoulli] |
✓ |
5.509 |
|
|
\[
{}y^{\prime } = \frac {-x^{2}+x +2+2 x^{3} \sqrt {x^{2}-4 x +4 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
1.997 |
|
|
\[
{}y^{\prime } = \frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (x +1\right ) y^{2}}
\] |
[_rational] |
✗ |
3.734 |
|
|
\[
{}y^{\prime } = -\frac {x^{2}+x +a x +a -2 \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.597 |
|
|
\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{2 x^{2}}+y^{3} {\mathrm e}^{3 x^{2}}\right ) {\mathrm e}^{-x^{2}} x
\] |
[_Abel] |
✓ |
2.149 |
|
|
\[
{}y^{\prime } = \frac {y \left (-{\mathrm e}^{x}+\ln \left (2 x \right ) x^{2} y-\ln \left (2 x \right ) x \right ) {\mathrm e}^{-x}}{x}
\] |
[_Bernoulli] |
✓ |
7.141 |
|
|
\[
{}y^{\prime } = \frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (x +1\right ) y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.393 |
|
|
\[
{}y^{\prime } = \frac {\left (18 x^{{3}/{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
4.799 |
|
|
\[
{}y^{\prime } = -\frac {y^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.342 |
|
|
\[
{}y^{\prime } = \frac {2 a}{y+2 a y^{4}-16 a^{2} x y^{2}+32 a^{3} x^{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.794 |
|
|
\[
{}y^{\prime } = -\frac {y^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.205 |
|
|
\[
{}y^{\prime } = \frac {-\ln \left (x \right )+2 \ln \left (2 x \right ) x y+\ln \left (2 x \right )+\ln \left (2 x \right ) y^{2}+\ln \left (2 x \right ) x^{2}}{\ln \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
4.836 |
|
|
\[
{}y^{\prime } = -\frac {b y a -b c +b^{2} x +b a \sqrt {x}-a^{2}}{a \left (a y-c +b x +a \sqrt {x}\right )}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.135 |
|
|
\[
{}y^{\prime } = \frac {\left (2 x +2+y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
1.510 |
|
|
\[
{}y^{\prime } = \frac {\left (x^{3}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.563 |
|
|
\[
{}y^{\prime } = \frac {y \left (x -y\right )}{x \left (x -y^{3}\right )}
\] |
[_rational] |
✓ |
1.302 |
|
|
\[
{}y^{\prime } = \frac {\left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}\right )^{3} {\mathrm e}^{x}}{4 \left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}+2\right ) \sqrt {y}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.809 |
|
|
\[
{}y^{\prime } = \frac {1+2 y}{x \left (-2+x y^{2}+2 x y^{3}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.536 |
|
|
\[
{}y^{\prime } = \frac {-x^{2}-x -a x -a +2 x^{3} \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
2.203 |
|
|
\[
{}y^{\prime } = \frac {2 x \sin \left (x \right )-\ln \left (2 x \right )+\ln \left (2 x \right ) x^{4}-2 \ln \left (2 x \right ) x^{2} y+\ln \left (2 x \right ) y^{2}}{\sin \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
100.342 |
|
|
\[
{}y^{\prime } = \frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{3}\right ) y}{x +1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.498 |
|
|
\[
{}y^{\prime } = \frac {\left (2 y \ln \left (x \right )-1\right )^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.993 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}+2 x +x^{4}-2 x^{2} y-1+y^{2}}{x +1}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.497 |
|
|
\[
{}y^{\prime } = \frac {x \left (-1+x -2 y x +2 x^{3}\right )}{x^{2}-y}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.027 |
|
|
\[
{}y^{\prime } = \frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 a^{2} x y^{2}+32 a^{3}}
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.007 |
|
|
\[
{}y^{\prime } = \frac {1+2 y}{x \left (-2+y x +2 x y^{2}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.216 |
|
|
\[
{}y^{\prime } = \frac {x +y^{4}-2 x^{2} y^{2}+x^{4}}{y}
\] |
[_rational] |
✗ |
1.563 |
|
|
\[
{}y^{\prime } = \frac {\left (a y^{2}+b \,x^{2}\right )^{3} x}{a^{{5}/{2}} \left (a y^{2}+b \,x^{2}+a \right ) y}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.097 |
|
|
\[
{}y^{\prime } = -\frac {\cos \left (y\right ) \left (x -\cos \left (y\right )+1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )}
\] |
[‘y=_G(x,y’)‘] |
✗ |
8.684 |
|
|
\[
{}y^{\prime } = -\frac {i \left (8 i x +16 y^{4}+8 x^{2} y^{2}+x^{4}\right )}{32 y}
\] |
[_rational] |
✗ |
0.721 |
|
|
\[
{}y^{\prime } = \frac {x}{-y+x^{4}+2 x^{2} y^{2}+y^{4}}
\] |
[_rational] |
✗ |
1.874 |
|
|
\[
{}y^{\prime } = \frac {\left (-1+y \ln \left (x \right )\right )^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.724 |
|
|
\[
{}y^{\prime } = -\frac {i \left (i x +x^{4}+2 x^{2} y^{2}+y^{4}\right )}{y}
\] |
[_rational] |
✗ |
0.696 |
|
|
\[
{}y^{\prime } = -\frac {y \left (\tan \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \left (x \right )}
\] |
[_Bernoulli] |
✓ |
20.474 |
|
|
\[
{}y^{\prime } = \frac {y \left (x +y\right )}{x \left (x +y^{3}\right )}
\] |
[_rational] |
✓ |
1.301 |
|
|
\[
{}y^{\prime } = \frac {\left (x -y\right )^{2} \left (x +y\right )^{2} x}{y}
\] |
[_rational] |
✗ |
1.400 |
|
|
\[
{}y^{\prime } = \frac {\left (x^{2}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.472 |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.393 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (y\right ) \left (\cos \left (y\right ) x^{3}-x -1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )}
\] |
[‘y=_G(x,y’)‘] |
✗ |
76.551 |
|
|
\[
{}y^{\prime } = \frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (x +1\right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
1.625 |
|
|
\[
{}y^{\prime } = \frac {y x +x^{3}+x y^{2}+y^{3}}{x^{2}}
\] |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
1.438 |
|
|
\[
{}y^{\prime } = \frac {y^{{3}/{2}}}{y^{{3}/{2}}+x^{2}-2 y x +y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
2.779 |
|
|
\[
{}y^{\prime } = \frac {2 x^{3} y+x^{6}+x^{2} y^{2}+y^{3}}{x^{4}}
\] |
[_rational, _Abel] |
✗ |
1.306 |
|
|
\[
{}y^{\prime } = \frac {-4 y x +x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.186 |
|
|
\[
{}y^{\prime } = \frac {\left (2 x +2+x^{3} y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
1.578 |
|
|
\[
{}y^{\prime } = -\frac {i \left (54 i x^{2}+81 y^{4}+18 x^{4} y^{2}+x^{8}\right ) x}{243 y}
\] |
[_rational] |
✗ |
0.801 |
|
|
\[
{}y^{\prime } = \frac {\left (x y^{2}+1\right )^{3}}{x^{4} \left (x y^{2}+1+x \right ) y}
\] |
[_rational] |
✗ |
1.441 |
|
|
\[
{}y^{\prime } = \frac {-4 y x -x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.200 |
|
|
\[
{}y^{\prime } = -\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-x \right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.646 |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x \right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.244 |
|
|
\[
{}y^{\prime } = \frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.490 |
|
|
\[
{}y^{\prime } = \frac {y \left (-1-\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x y\right )}{x}
\] |
[_Bernoulli] |
✓ |
20.909 |
|
|
\[
{}y^{\prime } = \frac {y \left (-\ln \left (x \right )-x \ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x^{2} y\right )}{x \ln \left (x \right )}
\] |
[_Bernoulli] |
✓ |
7.780 |
|
|
\[
{}y^{\prime } = \frac {-8 y x -x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.186 |
|