|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {y \left (1-x +y x^{2} \ln \left (x \right )+x^{3} y-\ln \left (x \right ) x -x^{2}\right )}{\left (-1+x \right ) x}
\] |
[_Bernoulli] |
✓ |
3.711 |
|
|
\[
{}y^{\prime } = \frac {y \ln \left (x \right ) x -y+2 x^{5} b +2 x^{3} a y^{2}}{\left (\ln \left (x \right ) x -1\right ) x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
9.037 |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right )+x +x^{3}+x^{4}\right ) y}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.223 |
|
|
\[
{}y^{\prime } = -\frac {\left (-\ln \left (y-1\right )+\ln \left (y+1\right )+2 \ln \left (x \right )\right ) x \left (y+1\right )^{2}}{8}
\] |
[‘y=_G(x,y’)‘] |
✗ |
24.866 |
|
|
\[
{}y^{\prime } = \frac {\left (-\ln \left (y-1\right )+\ln \left (y+1\right )+2 \ln \left (x \right )\right )^{2} x \left (y+1\right )^{2}}{16}
\] |
[‘y=_G(x,y’)‘] |
✗ |
53.222 |
|
|
\[
{}y^{\prime } = \frac {\left (-y^{2}+4 a x \right )^{3}}{\left (-y^{2}+4 a x -1\right ) y}
\] |
[_rational] |
✗ |
3.481 |
|
|
\[
{}y^{\prime } = \frac {2 a x +2 a +x^{3} \sqrt {-y^{2}+4 a x}}{\left (x +1\right ) y}
\] |
[‘y=_G(x,y’)‘] |
✗ |
47.092 |
|
|
\[
{}y^{\prime } = \frac {-\ln \left (x \right )+{\mathrm e}^{\frac {1}{x}}+4 x^{2} y+2 x +2 x y^{2}+2 x^{3}}{\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
217.693 |
|
|
\[
{}y^{\prime } = -\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-1\right ) y}{x +1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.110 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+2 x +1+2 x^{3} \sqrt {x^{2}+2 x +1-4 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
6.970 |
|
|
\[
{}y^{\prime } = \frac {-b y a +b^{2}+a b +b^{2} x -b a \sqrt {x}-a^{2}}{a \left (-a y+b +a +b x -a \sqrt {x}\right )}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.652 |
|
|
\[
{}y^{\prime } = -\frac {y \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}+y x^{2} \ln \left (x \right )+x^{3} y-\ln \left (x \right ) x -x^{2}\right )}{\left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right ) x}
\] |
[_Bernoulli] |
✓ |
4.264 |
|
|
\[
{}y^{\prime } = \frac {-x^{2}+x +2+2 x^{3} \sqrt {x^{2}-4 x +4 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
6.349 |
|
|
\[
{}y^{\prime } = \frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (x +1\right ) y^{2}}
\] |
[_rational] |
✗ |
39.999 |
|
|
\[
{}y^{\prime } = -\frac {x^{2}+x +a x +a -2 \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
3.028 |
|
|
\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{2 x^{2}}+y^{3} {\mathrm e}^{3 x^{2}}\right ) {\mathrm e}^{-x^{2}} x
\] |
[_Abel] |
✓ |
2.198 |
|
|
\[
{}y^{\prime } = \frac {y \left (-{\mathrm e}^{x}+\ln \left (2 x \right ) x^{2} y-\ln \left (2 x \right ) x \right ) {\mathrm e}^{-x}}{x}
\] |
[_Bernoulli] |
✓ |
5.811 |
|
|
\[
{}y^{\prime } = \frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (x +1\right ) y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
38.181 |
|
|
\[
{}y^{\prime } = \frac {\left (18 x^{{3}/{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
4.546 |
|
|
\[
{}y^{\prime } = -\frac {y^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.519 |
|
|
\[
{}y^{\prime } = \frac {2 a}{y+2 a y^{4}-16 a^{2} x y^{2}+32 a^{3} x^{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.573 |
|
|
\[
{}y^{\prime } = -\frac {y^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.454 |
|
|
\[
{}y^{\prime } = \frac {-\ln \left (x \right )+2 \ln \left (2 x \right ) x y+\ln \left (2 x \right )+\ln \left (2 x \right ) y^{2}+\ln \left (2 x \right ) x^{2}}{\ln \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
5.490 |
|
|
\[
{}y^{\prime } = -\frac {b y a -c b +b^{2} x +b a \sqrt {x}-a^{2}}{a \left (a y-c +b x +a \sqrt {x}\right )}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.414 |
|
|
\[
{}y^{\prime } = \frac {\left (2 x +2+y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
3.044 |
|
|
\[
{}y^{\prime } = \frac {\left (x^{3}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.768 |
|
|
\[
{}y^{\prime } = \frac {y \left (x -y\right )}{x \left (x -y^{3}\right )}
\] |
[_rational] |
✓ |
1.419 |
|
|
\[
{}y^{\prime } = \frac {\left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}\right )^{3} {\mathrm e}^{x}}{4 \left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}+2\right ) \sqrt {y}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
7.917 |
|
|
\[
{}y^{\prime } = \frac {2 y+1}{x \left (-2+x y^{2}+2 x y^{3}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.853 |
|
|
\[
{}y^{\prime } = \frac {-x^{2}-x -a x -a +2 x^{3} \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
7.483 |
|
|
\[
{}y^{\prime } = \frac {2 x \sin \left (x \right )-\ln \left (2 x \right )+\ln \left (2 x \right ) x^{4}-2 \ln \left (2 x \right ) x^{2} y+\ln \left (2 x \right ) y^{2}}{\sin \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
148.818 |
|
|
\[
{}y^{\prime } = \frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{3}\right ) y}{x +1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.165 |
|
|
\[
{}y^{\prime } = \frac {\left (-1+2 y \ln \left (x \right )\right )^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.911 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}+2 x +x^{4}-2 x^{2} y-1+y^{2}}{x +1}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
3.172 |
|
|
\[
{}y^{\prime } = \frac {x \left (-1+x -2 x y+2 x^{3}\right )}{x^{2}-y}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.372 |
|
|
\[
{}y^{\prime } = \frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 a^{2} x y^{2}+32 a^{3}}
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.942 |
|
|
\[
{}y^{\prime } = \frac {2 y+1}{x \left (-2+x y+2 x y^{2}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.489 |
|
|
\[
{}y^{\prime } = \frac {x +y^{4}-2 y^{2} x^{2}+x^{4}}{y}
\] |
[_rational] |
✗ |
3.217 |
|
|
\[
{}y^{\prime } = \frac {\left (a y^{2}+b \,x^{2}\right )^{3} x}{a^{{5}/{2}} \left (a y^{2}+b \,x^{2}+a \right ) y}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
4.476 |
|
|
\[
{}y^{\prime } = -\frac {\cos \left (y\right ) \left (x -\cos \left (y\right )+1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )}
\] |
unknown |
✗ |
56.113 |
|
|
\[
{}y^{\prime } = -\frac {i \left (8 i x +16 y^{4}+8 y^{2} x^{2}+x^{4}\right )}{32 y}
\] |
[_rational] |
✗ |
1.327 |
|
|
\[
{}y^{\prime } = \frac {x}{-y+x^{4}+2 y^{2} x^{2}+y^{4}}
\] |
[_rational] |
✗ |
3.166 |
|
|
\[
{}y^{\prime } = \frac {\left (-1+y \ln \left (x \right )\right )^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.823 |
|
|
\[
{}y^{\prime } = -\frac {i \left (i x +x^{4}+2 y^{2} x^{2}+y^{4}\right )}{y}
\] |
[_rational] |
✗ |
1.184 |
|
|
\[
{}y^{\prime } = -\frac {y \left (\tan \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \left (x \right )}
\] |
[_Bernoulli] |
✓ |
38.051 |
|
|
\[
{}y^{\prime } = \frac {y \left (x +y\right )}{x \left (x +y^{3}\right )}
\] |
[_rational] |
✓ |
1.413 |
|
|
\[
{}y^{\prime } = \frac {\left (x -y\right )^{2} \left (x +y\right )^{2} x}{y}
\] |
[_rational] |
✗ |
2.667 |
|
|
\[
{}y^{\prime } = \frac {\left (x^{2}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.579 |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.635 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (y\right ) \left (\cos \left (y\right ) x^{3}-x -1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )}
\] |
unknown |
✗ |
83.054 |
|
|
\[
{}y^{\prime } = \frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (x +1\right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
3.315 |
|
|
\[
{}y^{\prime } = \frac {x y+x^{3}+x y^{2}+y^{3}}{x^{2}}
\] |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
1.486 |
|
|
\[
{}y^{\prime } = \frac {y^{{3}/{2}}}{y^{{3}/{2}}+x^{2}-2 x y+y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
2.805 |
|
|
\[
{}y^{\prime } = \frac {2 x^{3} y+x^{6}+y^{2} x^{2}+y^{3}}{x^{4}}
\] |
[_rational, _Abel] |
✗ |
2.586 |
|
|
\[
{}y^{\prime } = \frac {-4 x y+x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.370 |
|
|
\[
{}y^{\prime } = \frac {\left (2 x +2+x^{3} y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
5.696 |
|
|
\[
{}y^{\prime } = -\frac {i \left (54 i x^{2}+81 y^{4}+18 x^{4} y^{2}+x^{8}\right ) x}{243 y}
\] |
[_rational] |
✗ |
1.438 |
|
|
\[
{}y^{\prime } = \frac {\left (1+x y^{2}\right )^{3}}{x^{4} \left (x y^{2}+1+x \right ) y}
\] |
[_rational] |
✗ |
3.497 |
|
|
\[
{}y^{\prime } = \frac {-4 x y-x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.372 |
|
|
\[
{}y^{\prime } = -\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-x \right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.388 |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x \right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.422 |
|
|
\[
{}y^{\prime } = \frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.271 |
|
|
\[
{}y^{\prime } = \frac {y \left (-1-\ln \left (\frac {\left (-1+x \right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (-1+x \right ) \left (x +1\right )}{x}\right ) x y\right )}{x}
\] |
[_Bernoulli] |
✓ |
14.410 |
|
|
\[
{}y^{\prime } = \frac {y \left (-\ln \left (x \right )-x \ln \left (\frac {\left (-1+x \right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (-1+x \right ) \left (x +1\right )}{x}\right ) x^{2} y\right )}{x \ln \left (x \right )}
\] |
[_Bernoulli] |
✓ |
5.464 |
|
|
\[
{}y^{\prime } = \frac {-8 x y-x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.387 |
|
|
\[
{}y^{\prime } = \frac {y \left (y+1\right )}{x \left (-y-1+x y\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.015 |
|
|
\[
{}y^{\prime } = -\frac {i \left (16 i x^{2}+16 y^{4}+8 x^{4} y^{2}+x^{8}\right ) x}{32 y}
\] |
[_rational] |
✗ |
1.414 |
|
|
\[
{}y^{\prime } = \frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 x^{2} y^{4}}
\] |
[_rational] |
✓ |
3.112 |
|
|
\[
{}y^{\prime } = \frac {-4 y a x -a^{2} x^{3}-2 a \,x^{2} b -4 a x +8}{8 y+2 a \,x^{2}+4 b x +8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.738 |
|
|
\[
{}y^{\prime } = \frac {\left (x +1+\ln \left (y\right ) x \right ) \ln \left (y\right ) y}{x \left (x +1\right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
3.571 |
|
|
\[
{}y^{\prime } = \frac {x y+x +y^{2}}{\left (-1+x \right ) \left (x +y\right )}
\] |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.056 |
|
|
\[
{}y^{\prime } = \frac {-4 x y-x^{3}-2 a \,x^{2}-4 x +8}{8 y+2 x^{2}+4 a x +8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.342 |
|
|
\[
{}y^{\prime } = \frac {x -y+\sqrt {y}}{x -y+\sqrt {y}+1}
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.636 |
|
|
\[
{}y^{\prime } = \frac {y \left (-\ln \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \ln \left (\frac {1}{x}\right )}
\] |
[_Bernoulli] |
✓ |
9.670 |
|
|
\[
{}y^{\prime } = \frac {y \left (y+1\right )}{x \left (-y-1+x y^{4}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.047 |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2} y+1+y^{2} x^{6}+y^{3} x^{9}}{x^{3}}
\] |
[_rational, _Abel] |
✗ |
2.612 |
|
|
\[
{}y^{\prime } = \frac {x^{3} y+x^{3}+x y^{2}+y^{3}}{\left (-1+x \right ) x^{3}}
\] |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
2.677 |
|
|
\[
{}y^{\prime } = \frac {x y+y+x \sqrt {x^{2}+y^{2}}}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
11.822 |
|
|
\[
{}y^{\prime } = \frac {\left (x^{4}+x^{3}+x +3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.901 |
|
|
\[
{}y^{\prime } = \frac {y \left (-\tanh \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \tanh \left (\frac {1}{x}\right )}
\] |
[_Bernoulli] |
✓ |
42.867 |
|
|
\[
{}y^{\prime } = -\frac {y \left (\tanh \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tanh \left (x \right )}
\] |
[_Bernoulli] |
✓ |
44.745 |
|
|
\[
{}y^{\prime } = \frac {-\sinh \left (x \right )+x^{2} \ln \left (x \right )+2 y \ln \left (x \right ) x +\ln \left (x \right )+y^{2} \ln \left (x \right )}{\sinh \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
31.436 |
|
|
\[
{}y^{\prime } = -\frac {\ln \left (x \right )-\sinh \left (x \right ) x^{2}-2 \sinh \left (x \right ) x y-\sinh \left (x \right )-\sinh \left (x \right ) y^{2}}{\ln \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
68.936 |
|
|
\[
{}y^{\prime } = \frac {y \ln \left (x \right )+\cosh \left (x \right ) x a y^{2}+\cosh \left (x \right ) x^{3} b}{x \ln \left (x \right )}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
47.458 |
|
|
\[
{}y^{\prime } = \frac {x \left (-x -1+x^{2}-2 x^{2} y+2 x^{4}\right )}{\left (x^{2}-y\right ) \left (x +1\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.293 |
|
|
\[
{}y^{\prime } = -\frac {y \left (\ln \left (-1+x \right )+\coth \left (x +1\right ) x -\coth \left (x +1\right ) x^{2} y\right )}{x \ln \left (-1+x \right )}
\] |
[_Bernoulli] |
✓ |
42.121 |
|
|
\[
{}y^{\prime } = -\frac {\ln \left (-1+x \right )-\coth \left (x +1\right ) x^{2}-2 \coth \left (x +1\right ) x y-\coth \left (x +1\right )-\coth \left (x +1\right ) y^{2}}{\ln \left (-1+x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
186.936 |
|
|
\[
{}y^{\prime } = \frac {2 x \ln \left (\frac {1}{-1+x}\right )-\coth \left (\frac {x +1}{-1+x}\right )+\coth \left (\frac {x +1}{-1+x}\right ) y^{2}-2 \coth \left (\frac {x +1}{-1+x}\right ) x^{2} y+\coth \left (\frac {x +1}{-1+x}\right ) x^{4}}{\ln \left (\frac {1}{-1+x}\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
352.082 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2} \cosh \left (\frac {1}{-1+x}\right )-2 x \cosh \left (\frac {1}{-1+x}\right )-1+y^{2}-2 x^{2} y+x^{4}-x +x y^{2}-2 x^{3} y+x^{5}}{\left (-1+x \right ) \cosh \left (\frac {1}{-1+x}\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
192.754 |
|
|
\[
{}y^{\prime } = \frac {y \left (-\cosh \left (\frac {1}{x +1}\right ) x +\cosh \left (\frac {1}{x +1}\right )-x +x^{2} y-x^{2}+x^{3} y\right )}{x \left (-1+x \right ) \cosh \left (\frac {1}{x +1}\right )}
\] |
[_Bernoulli] |
✓ |
9.704 |
|
|
\[
{}y^{\prime } = -\frac {y \left (1+x y\right )}{x \left (x y+1-y\right )}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.097 |
|
|
\[
{}y^{\prime } = \frac {y}{x \left (-1+y+x^{2} y^{3}+y^{4} x^{3}\right )}
\] |
[_rational] |
✗ |
7.414 |
|
|
\[
{}y^{\prime } = \frac {x^{3}+3 a \,x^{2}+3 a^{2} x +a^{3}+x y^{2}+a y^{2}+y^{3}}{\left (x +a \right )^{3}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
74.847 |
|
|
\[
{}y^{\prime } = \frac {y^{3} x \,{\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+3 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+9 y}
\] |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
4.434 |
|
|
\[
{}y^{\prime } = \frac {y \left (-1-\cosh \left (\frac {x +1}{-1+x}\right ) x +\cosh \left (\frac {x +1}{-1+x}\right ) x^{2} y-\cosh \left (\frac {x +1}{-1+x}\right ) x^{2}+\cosh \left (\frac {x +1}{-1+x}\right ) x^{3} y\right )}{x}
\] |
[_Bernoulli] |
✓ |
13.204 |
|
|
\[
{}y^{\prime } = \frac {\left (x +y+1\right ) y}{\left (2 y^{3}+y+x \right ) \left (x +1\right )}
\] |
[_rational] |
✗ |
2.683 |
|
|
\[
{}y^{\prime } = \frac {y \left (-1-x \,{\mathrm e}^{\frac {x +1}{-1+x}}+x^{2} {\mathrm e}^{\frac {x +1}{-1+x}} y-x^{2} {\mathrm e}^{\frac {x +1}{-1+x}}+x^{3} {\mathrm e}^{\frac {x +1}{-1+x}} y\right )}{x}
\] |
[_Bernoulli] |
✓ |
5.106 |
|
|
\[
{}y^{\prime } = \frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
76.034 |
|
|
\[
{}y^{\prime } = \frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2+2 y^{2} {\mathrm e}^{-\frac {x^{2}}{2}}+2 y^{3} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2}
\] |
[_Abel] |
✓ |
3.511 |
|
|
\[
{}y^{\prime } = -\frac {-\frac {1}{x}-\textit {\_F1} \left (y+\frac {1}{x}\right )}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
2.659 |
|