| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
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} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.140 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (x +1\right ) y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
201.472 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (18 x^{{3}/{2}}+36 y^{2}-12 x^{3} y+x^{6}\right ) \sqrt {x}}{36} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
7.207 |
|
| \begin{align*}
y^{\prime }&=-\frac {y^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
38.889 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a}{y+2 y^{4} a -16 a^{2} x y^{2}+32 a^{3} x^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.381 |
|
| \begin{align*}
y^{\prime }&=-\frac {y^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
37.100 |
|
| \begin{align*}
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}+x^{2} \ln \left (2 x \right )}{\ln \left (x \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
10.558 |
|
| \begin{align*}
y^{\prime }&=-\frac {a b y-b c +b^{2} x +b a \sqrt {x}-a^{2}}{a \left (a y-c +b x +a \sqrt {x}\right )} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
26.027 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (2 x +2+y\right ) y}{\left (-1+2 x +\ln \left (y\right )\right ) \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
✗ |
6.813 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x^{3}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.223 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (x -y\right )}{x \left (x -y^{3}\right )} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.593 |
|
| \begin{align*}
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}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
13.186 |
|
| \begin{align*}
y^{\prime }&=\frac {1+2 y}{x \left (-2+x y^{2}+2 x y^{3}\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.290 |
|
| \begin{align*}
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} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
13.037 |
|
| \begin{align*}
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 )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.599 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-x \ln \left (y\right )-\ln \left (y\right )+x^{3}\right ) y}{x +1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✓ |
5.949 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (2 y \ln \left (x \right )-1\right )^{3}}{\left (-1+2 y \ln \left (x \right )-y\right ) x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
54.206 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{2}+2 x +x^{4}-2 x^{2} y-1+y^{2}}{x +1} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
6.934 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (-1+x -2 y x +2 x^{3}\right )}{x^{2}-y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
3.441 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 a^{2} x y^{2}+32 a^{3}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
5.268 |
|
| \begin{align*}
y^{\prime }&=\frac {1+2 y}{x \left (-2+y x +2 x y^{2}\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.056 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y^{4}-2 x^{2} y^{2}+x^{4}}{y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.718 |
|
| \begin{align*}
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} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
16.582 |
|
| \begin{align*}
y^{\prime }&=-\frac {\cos \left (y\right ) \left (x -\cos \left (y\right )+1\right )}{\left (\sin \left (y\right ) x -1\right ) \left (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
76.715 |
|
| \begin{align*}
y^{\prime }&=-\frac {i \left (8 i x +16 y^{4}+8 x^{2} y^{2}+x^{4}\right )}{32 y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.881 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{-y+x^{4}+2 x^{2} y^{2}+y^{4}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.786 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-1+y \ln \left (x \right )\right )^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
69.211 |
|
| \begin{align*}
y^{\prime }&=-\frac {i \left (i x +x^{4}+2 x^{2} y^{2}+y^{4}\right )}{y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
5.479 |
|
| \begin{align*}
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 )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
7.506 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (x +y\right )}{x \left (y^{3}+x \right )} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.630 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x -y\right )^{2} \left (x +y\right )^{2} x}{y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
10.494 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x^{2}+3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.180 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x \ln \left (y\right )+\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.613 |
|
| \begin{align*}
y^{\prime }&=\frac {\cos \left (y\right ) \left (\cos \left (y\right ) x^{3}-x -1\right )}{\left (\sin \left (y\right ) x -1\right ) \left (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
46.159 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x +1+x^{4} \ln \left (y\right )\right ) y \ln \left (y\right )}{x \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✓ |
✓ |
✓ |
6.821 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +x^{3}+x y^{2}+y^{3}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
3.306 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{{3}/{2}}}{y^{{3}/{2}}+x^{2}-2 y x +y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
5.310 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{3} y+x^{6}+x^{2} y^{2}+y^{3}}{x^{4}} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
3.242 |
|
| \begin{align*}
y^{\prime }&=\frac {-4 y x +x^{3}+2 x^{2}-4 x -8}{-8 y+2 x^{2}+4 x -8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.661 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (2 x +2+x^{3} y\right ) y}{\left (-1+2 x +\ln \left (y\right )\right ) \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✓ |
✓ |
✗ |
7.050 |
|
| \begin{align*}
y^{\prime }&=-\frac {i \left (54 i x^{2}+81 y^{4}+18 y^{2} x^{4}+x^{8}\right ) x}{243 y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
7.391 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (1+x y^{2}\right )^{3}}{x^{4} \left (x y^{2}+1+x \right ) y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
10.099 |
|
| \begin{align*}
y^{\prime }&=\frac {-4 y x -x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.279 |
|
| \begin{align*}
y^{\prime }&=-\frac {\left (x \ln \left (y\right )+\ln \left (y\right )-x \right ) y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✓ |
23.225 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x \ln \left (y\right )+\ln \left (y\right )+x \right ) y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.161 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-x \ln \left (y\right )-\ln \left (y\right )+x^{4}\right ) y}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✓ |
6.505 |
|
| \begin{align*}
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} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.385 |
|
| \begin{align*}
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 )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
8.126 |
|
| \begin{align*}
y^{\prime }&=\frac {-8 y x -x^{3}+2 x^{2}-8 x +32}{32 y+4 x^{2}-8 x +32} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.803 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y+1\right )}{x \left (-y-1+y x \right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
71.059 |
|
| \begin{align*}
y^{\prime }&=-\frac {i \left (16 i x^{2}+16 y^{4}+8 y^{2} x^{4}+x^{8}\right ) x}{32 y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
7.071 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{6}}{y^{3}+2+16 x y^{2}+32 x^{2} y^{4}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
4.126 |
|
| \begin{align*}
y^{\prime }&=\frac {-4 a x y-a^{2} x^{3}-2 a b \,x^{2}-4 a x +8}{8 y+2 a \,x^{2}+4 b x +8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.337 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x +1+x \ln \left (y\right )\right ) \ln \left (y\right ) y}{x \left (x +1\right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✓ |
✓ |
✓ |
19.699 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +x +y^{2}}{\left (x -1\right ) \left (x +y\right )} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
7.951 |
|
| \begin{align*}
y^{\prime }&=\frac {-4 y x -x^{3}-2 a \,x^{2}-4 x +8}{8 y+2 x^{2}+4 a x +8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
12.749 |
|
| \begin{align*}
y^{\prime }&=\frac {x -y+\sqrt {y}}{x -y+\sqrt {y}+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
4.040 |
|
| \begin{align*}
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 )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
7.605 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y+1\right )}{x \left (-y-1+x y^{4}\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.717 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2} y+1+x^{6} y^{2}+y^{3} x^{9}}{x^{3}} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
3.244 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3} y+x^{3}+x y^{2}+y^{3}}{\left (x -1\right ) x^{3}} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✓ |
7.638 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +y+x \sqrt {x^{2}+y^{2}}}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
17.450 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x^{4}+x^{3}+x +3 y^{2}\right ) y}{\left (x +6 y^{2}\right ) x} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.691 |
|
| \begin{align*}
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 )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
9.166 |
|
| \begin{align*}
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 )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
7.220 |
|
| \begin{align*}
y^{\prime }&=\frac {-\sinh \left (x \right )+x^{2} \ln \left (x \right )+2 x y \ln \left (x \right )+\ln \left (x \right )+y^{2} \ln \left (x \right )}{\sinh \left (x \right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
26.126 |
|
| \begin{align*}
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 )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
56.125 |
|
| \begin{align*}
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 )} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.211 |
|
| \begin{align*}
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 )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
4.252 |
|
| \begin{align*}
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 )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
7.985 |
|
| \begin{align*}
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 )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✗ |
✓ |
✗ |
4.645 |
|
| \begin{align*}
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 )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✗ |
✓ |
✗ |
79.925 |
|
| \begin{align*}
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 )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
10.013 |
|
| \begin{align*}
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 )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
14.178 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (y x +1\right )}{x \left (y x +1-y\right )} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
19.227 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x \left (-1+y+x^{2} y^{3}+x^{3} y^{4}\right )} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.832 |
|
| \begin{align*}
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}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
3.151 |
|
| \begin{align*}
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} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
61.912 |
|
| \begin{align*}
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} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
11.449 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x +y+1\right ) y}{\left (x +y+2 y^{3}\right ) \left (x +1\right )} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
6.262 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-1-x \,{\mathrm e}^{\frac {x +1}{x -1}}+x^{2} {\mathrm e}^{\frac {x +1}{x -1}} y-x^{2} {\mathrm e}^{\frac {x +1}{x -1}}+x^{3} {\mathrm e}^{\frac {x +1}{x -1}} y\right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
9.422 |
|
| \begin{align*}
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}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
28.817 |
|
| \begin{align*}
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} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
11.031 |
|
| \begin{align*}
y^{\prime }&=-\frac {-\frac {1}{x}-\textit {\_F1} \left (y+\frac {1}{x}\right )}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
4.803 |
|
| \begin{align*}
y^{\prime }&=\frac {\textit {\_F1} \left (y^{2}-2 \ln \left (x \right )\right )}{\sqrt {y^{2}}\, x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
6.769 |
|
| \begin{align*}
y^{\prime }&=\frac {-x \sin \left (2 y\right )-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{4}+x^{4}}{2 x \left (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
11.468 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +y+x^{4} \sqrt {x^{2}+y^{2}}}{x \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
12.446 |
|
| \begin{align*}
y^{\prime }&=\frac {-x \sin \left (2 y\right )-\sin \left (2 y\right )+x \cos \left (2 y\right )+x}{2 x \left (x +1\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
78.584 |
|
| \begin{align*}
y^{\prime }&=-\frac {1}{-x -\textit {\_F1} \left (y-\ln \left (x \right )\right ) y \,{\mathrm e}^{y}} \\
\end{align*} |
[NONE] |
✗ |
✓ |
✓ |
✗ |
5.293 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (1+2 y\right ) \left (y+1\right )}{x \left (-2 y-2+x +2 y x \right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
84.898 |
|
| \begin{align*}
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}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
3.007 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y+y^{2}-2 x y \ln \left (x \right )+x^{2} \ln \left (x \right )^{2}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.209 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3} {\mathrm e}^{y}+x^{4}+y \,{\mathrm e}^{y}-{\mathrm e}^{y} \ln \left (x +{\mathrm e}^{y}\right )+y x -\ln \left (x +{\mathrm e}^{y}\right ) x +x}{x^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
34.917 |
|
| \begin{align*}
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} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
17.834 |
|
| \begin{align*}
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} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
15.220 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-3 x^{3} y-3+y^{2} x^{7}\right )}{x \left (x^{3} y+1\right )} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.777 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y+3\right )^{3} {\mathrm e}^{\frac {9 x^{2}}{2}} x \,{\mathrm e}^{\frac {3 x^{2}}{2}} {\mathrm e}^{-3 x^{2}}}{243 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+243 y} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
74.319 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (x -y\right )^{3} \left (x +y\right )^{3} x}{\left (x^{2}-y^{2}-1\right ) y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
12.682 |
|
| \begin{align*}
y^{\prime }&=\frac {-2 \cos \left (y\right )+x^{3} \cos \left (2 y\right ) \ln \left (x \right )+x^{3} \ln \left (x \right )}{2 \sin \left (y\right ) \ln \left (x \right ) x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✓ |
10.228 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x \left (-1+y x +x y^{3}+x y^{4}\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.816 |
|