|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {-x^{2}+1+4 x^{3} \sqrt {x^{2}-2 x +1+8 y}}{4 x +4}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
5.989 |
|
|
\[
{}y^{\prime } = \frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{3}+x^{3}}{2 x}
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.753 |
|
|
\[
{}y^{\prime } = \frac {y+x^{3} \sqrt {x^{2}+y^{2}}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.089 |
|
|
\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-2 b x}+y^{3} {\mathrm e}^{-3 b x}\right ) {\mathrm e}^{b x}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
1.636 |
|
|
\[
{}y^{\prime } = \frac {x +1+2 \sqrt {4 x^{2} y+1}\, x^{3}}{2 x^{3} \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
5.537 |
|
|
\[
{}y^{\prime } = \frac {y \ln \left (x -1\right )+x^{4}+x^{3}+x^{2} y^{2}+x y^{2}}{\ln \left (x -1\right ) x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
2.936 |
|
|
\[
{}y^{\prime } = \frac {y \ln \left (x -1\right )+{\mathrm e}^{x +1} x^{3}+7 \,{\mathrm e}^{x +1} x y^{2}}{\ln \left (x -1\right ) x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
4.068 |
|
|
\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+y^{3} {\mathrm e}^{-2 x}\right ) {\mathrm e}^{\frac {2 x}{3}}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
2.467 |
|
|
\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{-2 x}+y^{3} {\mathrm e}^{-3 x}\right ) {\mathrm e}^{x}
\] |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
1.874 |
|
|
\[
{}y^{\prime } = \frac {x \left (-2 x -2+3 x^{2} \sqrt {x^{2}+3 y}\right )}{3 x +3}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
5.309 |
|
|
\[
{}y^{\prime } = \frac {1}{x \left (x y^{2}+1+x \right ) y}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.942 |
|
|
\[
{}y^{\prime } = \frac {2 x \,{\mathrm e}^{x}-2 x -\ln \left (x \right )-1+x^{4} \ln \left (x \right )+x^{4}-2 y x^{2} \ln \left (x \right )-2 x^{2} y+y^{2} \ln \left (x \right )+y^{2}}{{\mathrm e}^{x}-1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
17.802 |
|
|
\[
{}y^{\prime } = \frac {-y \,{\mathrm e}^{x}+x y-x^{3} \ln \left (x \right )-x^{3}-x y^{2} \ln \left (x \right )-x y^{2}}{\left (-{\mathrm e}^{x}+x \right ) x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
3.663 |
|
|
\[
{}y^{\prime } = \frac {y \left (1-x +y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (x -1\right ) x}
\] |
[_Bernoulli] |
✓ |
3.481 |
|
|
\[
{}y^{\prime } = \frac {y \ln \left (x \right ) x -y+2 x^{5} b +2 x^{3} a y^{2}}{\left (x \ln \left (x \right )-1\right ) x}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
9.635 |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right )+x +x^{3}+x^{4}\right ) y}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.145 |
|
|
\[
{}y^{\prime } = -\frac {\left (-\ln \left (-1+y\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right ) x \left (1+y\right )^{2}}{8}
\] |
[‘y=_G(x,y’)‘] |
✗ |
19.087 |
|
|
\[
{}y^{\prime } = \frac {\left (-\ln \left (-1+y\right )+\ln \left (1+y\right )+2 \ln \left (x \right )\right )^{2} x \left (1+y\right )^{2}}{16}
\] |
[‘y=_G(x,y’)‘] |
✗ |
43.823 |
|
|
\[
{}y^{\prime } = \frac {\left (-y^{2}+4 a x \right )^{3}}{\left (-y^{2}+4 a x -1\right ) y}
\] |
[_rational] |
✗ |
3.066 |
|
|
\[
{}y^{\prime } = \frac {2 a x +2 a +x^{3} \sqrt {-y^{2}+4 a x}}{\left (x +1\right ) y}
\] |
[‘y=_G(x,y’)‘] |
✗ |
44.262 |
|
|
\[
{}y^{\prime } = \frac {-\ln \left (x \right )+{\mathrm e}^{\frac {1}{x}}+4 x^{2} y+2 x +2 x y^{2}+2 x^{3}}{\ln \left (x \right )-{\mathrm e}^{\frac {1}{x}}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
221.186 |
|
|
\[
{}y^{\prime } = -\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-1\right ) y}{x +1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
2.816 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+2 x +1+2 x^{3} \sqrt {x^{2}+2 x +1-4 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
6.168 |
|
|
\[
{}y^{\prime } = \frac {-b y a +b^{2}+a b +b^{2} x -b a \sqrt {x}-a^{2}}{a \left (-a y+b +a +b x -a \sqrt {x}\right )}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.533 |
|
|
\[
{}y^{\prime } = -\frac {y \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}+y x^{2} \ln \left (x \right )+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right ) x}
\] |
[_Bernoulli] |
✓ |
4.586 |
|
|
\[
{}y^{\prime } = \frac {-x^{2}+x +2+2 x^{3} \sqrt {x^{2}-4 x +4 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
5.658 |
|
|
\[
{}y^{\prime } = \frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (x +1\right ) y^{2}}
\] |
[_rational] |
✗ |
38.340 |
|
|
\[
{}y^{\prime } = -\frac {x^{2}+x +a x +a -2 \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.825 |
|
|
\[
{}y^{\prime } = \left (1+y^{2} {\mathrm e}^{2 x^{2}}+y^{3} {\mathrm e}^{3 x^{2}}\right ) {\mathrm e}^{-x^{2}} x
\] |
[_Abel] |
✓ |
2.446 |
|
|
\[
{}y^{\prime } = \frac {y \left (-{\mathrm e}^{x}+\ln \left (2 x \right ) x^{2} y-\ln \left (2 x \right ) x \right ) {\mathrm e}^{-x}}{x}
\] |
[_Bernoulli] |
✓ |
7.398 |
|
|
\[
{}y^{\prime } = \frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (x +1\right ) y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
38.056 |
|
|
\[
{}y^{\prime } = \frac {\left (18 x^{{3}/{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
4.444 |
|
|
\[
{}y^{\prime } = -\frac {y^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.473 |
|
|
\[
{}y^{\prime } = \frac {2 a}{y+2 a y^{4}-16 a^{2} x y^{2}+32 a^{3} x^{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.005 |
|
|
\[
{}y^{\prime } = -\frac {y^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.311 |
|
|
\[
{}y^{\prime } = \frac {-\ln \left (x \right )+2 \ln \left (2 x \right ) x y+\ln \left (2 x \right )+\ln \left (2 x \right ) y^{2}+\ln \left (2 x \right ) x^{2}}{\ln \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
5.389 |
|
|
\[
{}y^{\prime } = -\frac {b y a -b c +b^{2} x +b a \sqrt {x}-a^{2}}{a \left (a y-c +b x +a \sqrt {x}\right )}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.333 |
|
|
\[
{}y^{\prime } = \frac {\left (2 x +2+y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
3.043 |
|
|
\[
{}y^{\prime } = \frac {\left (x^{3}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.859 |
|
|
\[
{}y^{\prime } = \frac {y \left (x -y\right )}{x \left (x -y^{3}\right )}
\] |
[_rational] |
✓ |
1.471 |
|
|
\[
{}y^{\prime } = \frac {\left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}\right )^{3} {\mathrm e}^{x}}{4 \left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}+2\right ) \sqrt {y}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
7.498 |
|
|
\[
{}y^{\prime } = \frac {1+2 y}{x \left (-2+x y^{2}+2 x y^{3}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.900 |
|
|
\[
{}y^{\prime } = \frac {-x^{2}-x -a x -a +2 x^{3} \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 x +2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
6.699 |
|
|
\[
{}y^{\prime } = \frac {2 x \sin \left (x \right )-\ln \left (2 x \right )+\ln \left (2 x \right ) x^{4}-2 \ln \left (2 x \right ) x^{2} y+\ln \left (2 x \right ) y^{2}}{\sin \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
144.012 |
|
|
\[
{}y^{\prime } = \frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{3}\right ) y}{x +1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
2.993 |
|
|
\[
{}y^{\prime } = \frac {\left (-1+2 y \ln \left (x \right )\right )^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
3.049 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}+2 x +x^{4}-2 x^{2} y-1+y^{2}}{x +1}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.947 |
|
|
\[
{}y^{\prime } = \frac {x \left (-1+x -2 x y+2 x^{3}\right )}{x^{2}-y}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.103 |
|
|
\[
{}y^{\prime } = \frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 a^{2} x y^{2}+32 a^{3}}
\] |
[‘y=_G(x,y’)‘] |
✓ |
3.441 |
|
|
\[
{}y^{\prime } = \frac {1+2 y}{x \left (-2+x y+2 x y^{2}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.500 |
|
|
\[
{}y^{\prime } = \frac {x +y^{4}-2 x^{2} y^{2}+x^{4}}{y}
\] |
[_rational] |
✗ |
3.519 |
|
|
\[
{}y^{\prime } = \frac {\left (a y^{2}+b \,x^{2}\right )^{3} x}{a^{{5}/{2}} \left (a y^{2}+b \,x^{2}+a \right ) y}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
4.044 |
|
|
\[
{}y^{\prime } = -\frac {\cos \left (y\right ) \left (x -\cos \left (y\right )+1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )}
\] |
unknown |
✗ |
54.012 |
|
|
\[
{}y^{\prime } = -\frac {i \left (8 i x +16 y^{4}+8 x^{2} y^{2}+x^{4}\right )}{32 y}
\] |
[_rational] |
✗ |
1.299 |
|
|
\[
{}y^{\prime } = \frac {x}{-y+x^{4}+2 x^{2} y^{2}+y^{4}}
\] |
[_rational] |
✗ |
3.889 |
|
|
\[
{}y^{\prime } = \frac {\left (-1+y \ln \left (x \right )\right )^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.615 |
|
|
\[
{}y^{\prime } = -\frac {i \left (i x +x^{4}+2 x^{2} y^{2}+y^{4}\right )}{y}
\] |
[_rational] |
✗ |
1.301 |
|
|
\[
{}y^{\prime } = -\frac {y \left (\tan \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \left (x \right )}
\] |
[_Bernoulli] |
✓ |
12.455 |
|
|
\[
{}y^{\prime } = \frac {y \left (x +y\right )}{x \left (x +y^{3}\right )}
\] |
[_rational] |
✓ |
1.507 |
|
|
\[
{}y^{\prime } = \frac {\left (x -y\right )^{2} \left (x +y\right )^{2} x}{y}
\] |
[_rational] |
✗ |
2.842 |
|
|
\[
{}y^{\prime } = \frac {\left (x^{2}+3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.707 |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.630 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (y\right ) \left (\cos \left (y\right ) x^{3}-x -1\right )}{\left (x \sin \left (y\right )-1\right ) \left (x +1\right )}
\] |
unknown |
✗ |
81.647 |
|
|
\[
{}y^{\prime } = \frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (x +1\right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
3.301 |
|
|
\[
{}y^{\prime } = \frac {x y+x^{3}+x y^{2}+y^{3}}{x^{2}}
\] |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
1.618 |
|
|
\[
{}y^{\prime } = \frac {y^{{3}/{2}}}{y^{{3}/{2}}+x^{2}-2 x y+y^{2}}
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.149 |
|
|
\[
{}y^{\prime } = \frac {2 x^{3} y+x^{6}+x^{2} y^{2}+y^{3}}{x^{4}}
\] |
[_rational, _Abel] |
✗ |
2.454 |
|
|
\[
{}y^{\prime } = \frac {-4 x y+x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.389 |
|
|
\[
{}y^{\prime } = \frac {\left (2 x +2+x^{3} y\right ) y}{\left (\ln \left (y\right )+2 x -1\right ) \left (x +1\right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
5.493 |
|
|
\[
{}y^{\prime } = -\frac {i \left (54 i x^{2}+81 y^{4}+18 y^{2} x^{4}+x^{8}\right ) x}{243 y}
\] |
[_rational] |
✗ |
1.315 |
|
|
\[
{}y^{\prime } = \frac {\left (x y^{2}+1\right )^{3}}{x^{4} \left (x y^{2}+1+x \right ) y}
\] |
[_rational] |
✗ |
2.968 |
|
|
\[
{}y^{\prime } = \frac {-4 x y-x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.381 |
|
|
\[
{}y^{\prime } = -\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-x \right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.199 |
|
|
\[
{}y^{\prime } = \frac {\left (\ln \left (y\right ) x +\ln \left (y\right )+x \right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.438 |
|
|
\[
{}y^{\prime } = \frac {\left (-\ln \left (y\right ) x -\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.002 |
|
|
\[
{}y^{\prime } = \frac {y \left (-1-\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x y\right )}{x}
\] |
[_Bernoulli] |
✓ |
16.892 |
|
|
\[
{}y^{\prime } = \frac {y \left (-\ln \left (x \right )-x \ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (x -1\right ) \left (x +1\right )}{x}\right ) x^{2} y\right )}{x \ln \left (x \right )}
\] |
[_Bernoulli] |
✓ |
5.227 |
|
|
\[
{}y^{\prime } = \frac {-8 x y-x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.393 |
|
|
\[
{}y^{\prime } = \frac {y \left (1+y\right )}{x \left (-y-1+x y\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.829 |
|
|
\[
{}y^{\prime } = -\frac {i \left (16 i x^{2}+16 y^{4}+8 y^{2} x^{4}+x^{8}\right ) x}{32 y}
\] |
[_rational] |
✗ |
1.279 |
|
|
\[
{}y^{\prime } = \frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 x^{2} y^{4}}
\] |
[_rational] |
✓ |
3.393 |
|
|
\[
{}y^{\prime } = \frac {-4 y a x -a^{2} x^{3}-2 a \,x^{2} b -4 a x +8}{8 y+2 a \,x^{2}+4 b x +8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.799 |
|
|
\[
{}y^{\prime } = \frac {\left (x +1+\ln \left (y\right ) x \right ) \ln \left (y\right ) y}{x \left (x +1\right )}
\] |
[‘x=_G(y,y’)‘] |
✗ |
3.256 |
|
|
\[
{}y^{\prime } = \frac {x y+x +y^{2}}{\left (x -1\right ) \left (x +y\right )}
\] |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.034 |
|
|
\[
{}y^{\prime } = \frac {-4 x y-x^{3}-2 a \,x^{2}-4 x +8}{8 y+2 x^{2}+4 a x +8}
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.443 |
|
|
\[
{}y^{\prime } = \frac {x -y+\sqrt {y}}{x -y+\sqrt {y}+1}
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.583 |
|
|
\[
{}y^{\prime } = \frac {y \left (-\ln \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \ln \left (\frac {1}{x}\right )}
\] |
[_Bernoulli] |
✓ |
8.113 |
|
|
\[
{}y^{\prime } = \frac {y \left (1+y\right )}{x \left (-y-1+x y^{4}\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.320 |
|
|
\[
{}y^{\prime } = \frac {-3 x^{2} y+1+y^{2} x^{6}+y^{3} x^{9}}{x^{3}}
\] |
[_rational, _Abel] |
✗ |
2.472 |
|
|
\[
{}y^{\prime } = \frac {x^{3} y+x^{3}+x y^{2}+y^{3}}{\left (x -1\right ) x^{3}}
\] |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
2.845 |
|
|
\[
{}y^{\prime } = \frac {x y+y+x \sqrt {x^{2}+y^{2}}}{x \left (x +1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
11.556 |
|
|
\[
{}y^{\prime } = \frac {\left (x^{4}+x^{3}+x +3 y^{2}\right ) y}{\left (6 y^{2}+x \right ) x}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.138 |
|
|
\[
{}y^{\prime } = \frac {y \left (-\tanh \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \tanh \left (\frac {1}{x}\right )}
\] |
[_Bernoulli] |
✓ |
42.931 |
|
|
\[
{}y^{\prime } = -\frac {y \left (\tanh \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tanh \left (x \right )}
\] |
[_Bernoulli] |
✓ |
42.361 |
|
|
\[
{}y^{\prime } = \frac {-\sinh \left (x \right )+x^{2} \ln \left (x \right )+2 y \ln \left (x \right ) x +\ln \left (x \right )+y^{2} \ln \left (x \right )}{\sinh \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
27.204 |
|
|
\[
{}y^{\prime } = -\frac {\ln \left (x \right )-\sinh \left (x \right ) x^{2}-2 \sinh \left (x \right ) x y-\sinh \left (x \right )-\sinh \left (x \right ) y^{2}}{\ln \left (x \right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
86.119 |
|
|
\[
{}y^{\prime } = \frac {y \ln \left (x \right )+\cosh \left (x \right ) x a y^{2}+\cosh \left (x \right ) x^{3} b}{x \ln \left (x \right )}
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
47.849 |
|
|
\[
{}y^{\prime } = \frac {x \left (-x -1+x^{2}-2 x^{2} y+2 x^{4}\right )}{\left (x^{2}-y\right ) \left (x +1\right )}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.182 |
|
|
\[
{}y^{\prime } = -\frac {y \left (\ln \left (x -1\right )+\coth \left (x +1\right ) x -\coth \left (x +1\right ) x^{2} y\right )}{x \ln \left (x -1\right )}
\] |
[_Bernoulli] |
✓ |
42.187 |
|
|
\[
{}y^{\prime } = -\frac {\ln \left (x -1\right )-\coth \left (x +1\right ) x^{2}-2 \coth \left (x +1\right ) x y-\coth \left (x +1\right )-\coth \left (x +1\right ) y^{2}}{\ln \left (x -1\right )}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
186.904 |
|