|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = -\frac {y \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}+y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right ) x}
\] |
[_Bernoulli] |
✓ |
4.112 |
|
|
\[
{}y^{\prime } = \frac {-x^{2}+x +2+2 x^{3} \sqrt {x^{2}-4 x +4 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
5.675 |
|
|
\[
{}y^{\prime } = \frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (x +1\right ) y^{2}}
\] |
[_rational] |
✗ |
38.407 |
|
|
\[
{}y^{\prime } = -\frac {x^{2}+x +a x +a -2 \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.633 |
|
|
\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{2 x^{2}}+y^{3} {\mathrm e}^{3 x^{2}}\right ) {\mathrm e}^{-x^{2}} x
\] |
[_Abel] |
✓ |
2.204 |
|
|
\[
{}y^{\prime } = \frac {y \left (-{\mathrm e}^{x}+\ln \left (2 x \right ) x^{2} y-\ln \left (2 x \right ) x \right ) {\mathrm e}^{-x}}{x}
\] |
[_Bernoulli] |
✓ |
6.671 |
|
|
\[
{}y^{\prime } = \frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (x +1\right ) y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
37.375 |
|
|
\[
{}y^{\prime } = \frac {\left (18 x^{{3}/{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
4.223 |
|
|
\[
{}y^{\prime } = -\frac {y^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.308 |
|
|
\[
{}y^{\prime } = \frac {2 a}{y+2 a y^{4}-16 a^{2} x y^{2}+32 a^{3} x^{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.848 |
|
|
\[
{}y^{\prime } = -\frac {y^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.209 |
|
|
\[
{}y^{\prime } = \frac {-\ln \left (x \right )+2 \ln \left (2 x \right ) x y+\ln \left (2 x \right )+\ln \left (2 x \right ) y^{2}+\ln \left (2 x \right ) x^{2}}{\ln \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
5.118 |
|
|
\[
{}y^{\prime } = -\frac {b y a -b c +b^{2} x +b a \sqrt {x}-a^{2}}{a \left (a y-c +b x +a \sqrt {x}\right )}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.151 |
|
|
\[
{}y^{\prime } = \frac {\left (2 x +2+y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
2.907 |
|
|
\[
{}y^{\prime } = \frac {\left (x^{3}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.629 |
|
|
\[
{}y^{\prime } = \frac {y \left (x -y\right )}{x \left (x -y^{3}\right )}
\] |
[_rational] |
✓ |
1.372 |
|
|
\[
{}y^{\prime } = \frac {\left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}\right )^{3} {\mathrm e}^{x}}{4 \left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}+2\right ) \sqrt {y}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
6.950 |
|
|
\[
{}y^{\prime } = \frac {1+2 y}{x \left (-2+x y^{2}+2 x y^{3}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.574 |
|
|
\[
{}y^{\prime } = \frac {-x^{2}-x -a x -a +2 x^{3} \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
6.731 |
|
|
\[
{}y^{\prime } = \frac {2 x \sin \left (x \right )-\ln \left (2 x \right )+\ln \left (2 x \right ) x^{4}-2 \ln \left (2 x \right ) x^{2} y+\ln \left (2 x \right ) y^{2}}{\sin \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
136.747 |
|
|
\[
{}y^{\prime } = \frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{3}\right ) y}{x +1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
2.946 |
|
|
\[
{}y^{\prime } = \frac {\left (-1+2 y \ln \left (x \right )\right )^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.949 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}+2 x +x^{4}-2 x^{2} y-1+y^{2}}{x +1}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.676 |
|
|
\[
{}y^{\prime } = \frac {x \left (-1+x -2 x y+2 x^{3}\right )}{x^{2}-y}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.202 |
|
|
\[
{}y^{\prime } = \frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 a^{2} x y^{2}+32 a^{3}}
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.066 |
|
|
\[
{}y^{\prime } = \frac {1+2 y}{x \left (-2+x y+2 x y^{2}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.314 |
|
|
\[
{}y^{\prime } = \frac {x +y^{4}-2 y^{2} x^{2}+x^{4}}{y}
\] |
[_rational] |
✗ |
3.486 |
|
|
\[
{}y^{\prime } = \frac {\left (y^{2} a +b \,x^{2}\right )^{3} x}{a^{{5}/{2}} \left (y^{2} a +b \,x^{2}+a \right ) y}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
3.987 |
|
|
\[
{}y^{\prime } = -\frac {\cos \left (y\right ) \left (x -\cos \left (y\right )+1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )}
\] |
[‘y=_G(x,y’)‘] |
✗ |
53.773 |
|
|
\[
{}y^{\prime } = -\frac {i \left (8 i x +16 y^{4}+8 y^{2} x^{2}+x^{4}\right )}{32 y}
\] |
[_rational] |
✗ |
1.231 |
|
|
\[
{}y^{\prime } = \frac {x}{-y+x^{4}+2 y^{2} x^{2}+y^{4}}
\] |
[_rational] |
✗ |
3.506 |
|
|
\[
{}y^{\prime } = \frac {\left (-1+y \ln \left (x \right )\right )^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.622 |
|
|
\[
{}y^{\prime } = -\frac {i \left (i x +x^{4}+2 y^{2} x^{2}+y^{4}\right )}{y}
\] |
[_rational] |
✗ |
1.161 |
|
|
\[
{}y^{\prime } = -\frac {y \left (\tan \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \left (x \right )}
\] |
[_Bernoulli] |
✓ |
12.095 |
|
|
\[
{}y^{\prime } = \frac {y \left (x +y\right )}{x \left (x +y^{3}\right )}
\] |
[_rational] |
✓ |
1.354 |
|
|
\[
{}y^{\prime } = \frac {\left (x -y\right )^{2} \left (x +y\right )^{2} x}{y}
\] |
[_rational] |
✗ |
2.511 |
|
|
\[
{}y^{\prime } = \frac {\left (x^{2}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.544 |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.424 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (y\right ) \left (\cos \left (y\right ) x^{3}-x -1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )}
\] |
[‘y=_G(x,y’)‘] |
✗ |
81.319 |
|
|
\[
{}y^{\prime } = \frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (x +1\right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
3.393 |
|
|
\[
{}y^{\prime } = \frac {x y+x^{3}+x y^{2}+y^{3}}{x^{2}}
\] |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
1.465 |
|
|
\[
{}y^{\prime } = \frac {y^{{3}/{2}}}{y^{{3}/{2}}+x^{2}-2 x y+y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
2.834 |
|
|
\[
{}y^{\prime } = \frac {2 x^{3} y+x^{6}+y^{2} x^{2}+y^{3}}{x^{4}}
\] |
[_rational, _Abel] |
✗ |
2.547 |
|
|
\[
{}y^{\prime } = \frac {-4 x y+x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.234 |
|
|
\[
{}y^{\prime } = \frac {\left (2 x +2+x^{3} y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
5.519 |
|
|
\[
{}y^{\prime } = -\frac {i \left (54 i x^{2}+81 y^{4}+18 x^{4} y^{2}+x^{8}\right ) x}{243 y}
\] |
[_rational] |
✗ |
1.316 |
|
|
\[
{}y^{\prime } = \frac {\left (x y^{2}+1\right )^{3}}{x^{4} \left (x y^{2}+1+x \right ) y}
\] |
[_rational] |
✗ |
3.112 |
|
|
\[
{}y^{\prime } = \frac {-4 x y-x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.266 |
|
|
\[
{}y^{\prime } = -\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-x \right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.237 |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x \right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.247 |
|
|
\[
{}y^{\prime } = \frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.253 |
|
|
\[
{}y^{\prime } = \frac {y \left (-1-\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x y\right )}{x}
\] |
[_Bernoulli] |
✓ |
13.862 |
|
|
\[
{}y^{\prime } = \frac {y \left (-\ln \left (x \right )-x \ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x^{2} y\right )}{x \ln \left (x \right )}
\] |
[_Bernoulli] |
✓ |
5.014 |
|
|
\[
{}y^{\prime } = \frac {-8 x y-x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.264 |
|
|
\[
{}y^{\prime } = \frac {y \left (1+y\right )}{x \left (-y-1+x y\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.669 |
|
|
\[
{}y^{\prime } = -\frac {i \left (16 i x^{2}+16 y^{4}+8 x^{4} y^{2}+x^{8}\right ) x}{32 y}
\] |
[_rational] |
✗ |
1.306 |
|
|
\[
{}y^{\prime } = \frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 x^{2} y^{4}}
\] |
[_rational] |
✓ |
3.125 |
|
|
\[
{}y^{\prime } = \frac {-4 a x y-a^{2} x^{3}-2 a \,x^{2} b -4 a x +8}{8 y+2 x^{2} a +4 b x +8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.711 |
|
|
\[
{}y^{\prime } = \frac {\left (x +1+\ln \left (y\right ) x \right ) \ln \left (y\right ) y}{x \left (x +1\right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
3.381 |
|
|
\[
{}y^{\prime } = \frac {x y+x +y^{2}}{\left (x -1\right ) \left (x +y\right )}
\] |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.699 |
|
|
\[
{}y^{\prime } = \frac {-4 x y-x^{3}-2 x^{2} a -4 x +8}{8 y+2 x^{2}+4 a x +8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.358 |
|
|
\[
{}y^{\prime } = \frac {x -y+\sqrt {y}}{x -y+\sqrt {y}+1}
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.515 |
|
|
\[
{}y^{\prime } = \frac {y \left (-\ln \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \ln \left (\frac {1}{x}\right )}
\] |
[_Bernoulli] |
✓ |
7.507 |
|
|
\[
{}y^{\prime } = \frac {y \left (1+y\right )}{x \left (-y-1+x y^{4}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.989 |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2} y+1+x^{6} y^{2}+y^{3} x^{9}}{x^{3}}
\] |
[_rational, _Abel] |
✗ |
2.542 |
|
|
\[
{}y^{\prime } = \frac {x^{3} y+x^{3}+x y^{2}+y^{3}}{\left (x -1\right ) x^{3}}
\] |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
2.579 |
|
|
\[
{}y^{\prime } = \frac {x y+y+x \sqrt {y^{2}+x^{2}}}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
10.778 |
|
|
\[
{}y^{\prime } = \frac {\left (x^{4}+x^{3}+x +3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.885 |
|
|
\[
{}y^{\prime } = \frac {y \left (-\tanh \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \tanh \left (\frac {1}{x}\right )}
\] |
[_Bernoulli] |
✓ |
42.089 |
|
|
\[
{}y^{\prime } = -\frac {y \left (\tanh \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tanh \left (x \right )}
\] |
[_Bernoulli] |
✓ |
41.764 |
|
|
\[
{}y^{\prime } = \frac {-\sinh \left (x \right )+x^{2} \ln \left (x \right )+2 y \ln \left (x \right ) x +\ln \left (x \right )+y^{2} \ln \left (x \right )}{\sinh \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
27.234 |
|
|
\[
{}y^{\prime } = -\frac {\ln \left (x \right )-\sinh \left (x \right ) x^{2}-2 \sinh \left (x \right ) x y-\sinh \left (x \right )-\sinh \left (x \right ) y^{2}}{\ln \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
74.734 |
|
|
\[
{}y^{\prime } = \frac {y \ln \left (x \right )+\cosh \left (x \right ) x a y^{2}+\cosh \left (x \right ) x^{3} b}{x \ln \left (x \right )}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
38.230 |
|
|
\[
{}y^{\prime } = \frac {x \left (-x -1+x^{2}-2 x^{2} y+2 x^{4}\right )}{\left (x^{2}-y\right ) \left (x +1\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.222 |
|
|
\[
{}y^{\prime } = -\frac {y \left (\ln \left (x -1\right )+\coth \left (x +1\right ) x -\coth \left (x +1\right ) x^{2} y\right )}{x \ln \left (x -1\right )}
\] |
[_Bernoulli] |
✓ |
41.195 |
|
|
\[
{}y^{\prime } = -\frac {\ln \left (x -1\right )-\coth \left (x +1\right ) x^{2}-2 \coth \left (x +1\right ) x y-\coth \left (x +1\right )-\coth \left (x +1\right ) y^{2}}{\ln \left (x -1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
191.980 |
|
|
\[
{}y^{\prime } = \frac {2 x \ln \left (\frac {1}{x -1}\right )-\coth \left (\frac {x +1}{x -1}\right )+\coth \left (\frac {x +1}{x -1}\right ) y^{2}-2 \coth \left (\frac {x +1}{x -1}\right ) x^{2} y+\coth \left (\frac {x +1}{x -1}\right ) x^{4}}{\ln \left (\frac {1}{x -1}\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
341.682 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2} \cosh \left (\frac {1}{x -1}\right )-2 x \cosh \left (\frac {1}{x -1}\right )-1+y^{2}-2 x^{2} y+x^{4}-x +x y^{2}-2 x^{3} y+x^{5}}{\left (x -1\right ) \cosh \left (\frac {1}{x -1}\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
145.532 |
|
|
\[
{}y^{\prime } = \frac {y \left (-\cosh \left (\frac {1}{x +1}\right ) x +\cosh \left (\frac {1}{x +1}\right )-x +x^{2} y-x^{2}+x^{3} y\right )}{x \left (x -1\right ) \cosh \left (\frac {1}{x +1}\right )}
\] |
[_Bernoulli] |
✓ |
8.809 |
|
|
\[
{}y^{\prime } = -\frac {y \left (x y+1\right )}{x \left (x y+1-y\right )}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.827 |
|
|
\[
{}y^{\prime } = \frac {y}{x \left (-1+y+x^{2} y^{3}+y^{4} x^{3}\right )}
\] |
[_rational] |
✗ |
7.423 |
|
|
\[
{}y^{\prime } = \frac {x^{3}+3 x^{2} a +3 a^{2} x +a^{3}+x y^{2}+y^{2} a +y^{3}}{\left (x +a \right )^{3}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
72.873 |
|
|
\[
{}y^{\prime } = \frac {y^{3} x \,{\mathrm e}^{3 x^{2}} {\mathrm e}^{-\frac {9 x^{2}}{2}}}{9 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+3 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+9 y}
\] |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
4.098 |
|
|
\[
{}y^{\prime } = \frac {y \left (-1-\cosh \left (\frac {x +1}{x -1}\right ) x +\cosh \left (\frac {x +1}{x -1}\right ) x^{2} y-\cosh \left (\frac {x +1}{x -1}\right ) x^{2}+\cosh \left (\frac {x +1}{x -1}\right ) x^{3} y\right )}{x}
\] |
[_Bernoulli] |
✓ |
13.081 |
|
|
\[
{}y^{\prime } = \frac {\left (x +y+1\right ) y}{\left (2 y^{3}+y+x \right ) \left (x +1\right )}
\] |
[_rational] |
✗ |
2.587 |
|
|
\[
{}y^{\prime } = \frac {y \left (-1-x \,{\mathrm e}^{\frac {x +1}{x -1}}+x^{2} {\mathrm e}^{\frac {x +1}{x -1}} y-{\mathrm e}^{\frac {x +1}{x -1}} x^{2}+x^{3} {\mathrm e}^{\frac {x +1}{x -1}} y\right )}{x}
\] |
[_Bernoulli] |
✓ |
4.832 |
|
|
\[
{}y^{\prime } = \frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
74.838 |
|
|
\[
{}y^{\prime } = \frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2+2 y^{2} {\mathrm e}^{-\frac {x^{2}}{2}}+2 y^{3} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2}
\] |
[_Abel] |
✓ |
3.831 |
|
|
\[
{}y^{\prime } = -\frac {-\frac {1}{x}-\textit {\_F1} \left (y+\frac {1}{x}\right )}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
2.396 |
|
|
\[
{}y^{\prime } = \frac {\textit {\_F1} \left (y^{2}-2 \ln \left (x \right )\right )}{\sqrt {y^{2}}\, x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
2.981 |
|
|
\[
{}y^{\prime } = \frac {-\sin \left (2 y\right ) x -\sin \left (2 y\right )+\cos \left (2 y\right ) x^{4}+x^{4}}{2 x \left (x +1\right )}
\] |
[‘y=_G(x,y’)‘] |
✗ |
19.471 |
|
|
\[
{}y^{\prime } = \frac {x y+y+x^{4} \sqrt {y^{2}+x^{2}}}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
6.821 |
|
|
\[
{}y^{\prime } = \frac {-\sin \left (2 y\right ) x -\sin \left (2 y\right )+x \cos \left (2 y\right )+x}{2 x \left (x +1\right )}
\] |
[‘y=_G(x,y’)‘] |
✗ |
10.721 |
|
|
\[
{}y^{\prime } = -\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}}
\] |
[NONE] |
✗ |
3.136 |
|
|
\[
{}y^{\prime } = \frac {\left (1+2 y\right ) \left (1+y\right )}{x \left (-2 y-2+x +2 x y\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.945 |
|
|
\[
{}y^{\prime } = \frac {-125+300 x -240 x^{2}+64 x^{3}-80 y^{2}+64 x y^{2}+64 y^{3}}{\left (4 x -5\right )^{3}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
80.000 |
|
|
\[
{}y^{\prime } = \frac {x +y+y^{2}-2 y \ln \left (x \right ) x +x^{2} \ln \left (x \right )^{2}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
1.889 |
|
|
\[
{}y^{\prime } = \frac {x^{3} {\mathrm e}^{y}+x^{4}+{\mathrm e}^{y} y-{\mathrm e}^{y} \ln \left ({\mathrm e}^{y}+x \right )+x y-\ln \left ({\mathrm e}^{y}+x \right ) x +x}{x^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
38.668 |
|
|
\[
{}y^{\prime } = \frac {x^{2}}{2}+\sqrt {x^{3}-6 y}+x^{2} \sqrt {x^{3}-6 y}+x^{3} \sqrt {x^{3}-6 y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
45.147 |
|
|
\[
{}y^{\prime } = \frac {\left (-\sqrt {a}\, x^{3}+2 \sqrt {a \,x^{4}+8 y}+2 x^{2} \sqrt {a \,x^{4}+8 y}+2 x^{3} \sqrt {a \,x^{4}+8 y}\right ) \sqrt {a}}{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
38.224 |
|