| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=\frac {\left (1+y\right ) \left (\left (y-\ln \left (1+y\right )-\ln \left (x \right )\right ) x +1\right )}{y x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✓ |
57.516 |
|
| \begin{align*}
y^{\prime }&=\frac {6 y}{8 y^{4}+9 y^{3}+12 y^{2}+6 y-F \left (-\frac {y^{4}}{3}-\frac {y^{3}}{2}-y^{2}-y+x \right )} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✓ |
✓ |
✗ |
6.563 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
6.312 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y+\sqrt {x}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
97.904 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y+2+\sqrt {1+3 x}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
52.557 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{y+x^{{3}/{2}}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
87.459 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{{5}/{3}}}{y+x^{{4}/{3}}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
202.844 |
|
| \begin{align*}
y^{\prime }&=\frac {i x^{2} \left (i-2 \sqrt {-x^{3}+6 y}\right )}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
1.856 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y+\sqrt {x^{2}+1}} \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
112.940 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-1+y \ln \left (x \right )\right )^{2}}{x} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
2.955 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (-2+3 \sqrt {x^{2}+3 y}\right )}{3} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
21.866 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (2 y \ln \left (x \right )-1\right )^{2}}{x} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
42.029 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{b x}}{y \,{\mathrm e}^{-b x}+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
8.810 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} \left (1+2 \sqrt {x^{3}-6 y}\right )}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
21.450 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x}}{{\mathrm e}^{-x} y+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
9.001 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{\frac {2 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
39.717 |
|
| \begin{align*}
y^{\prime }&=\frac {1+2 x^{5} \sqrt {4 x^{2} y+1}}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
74.612 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (x +2 \sqrt {x^{3}-6 y}\right )}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
12.219 |
|
| \begin{align*}
y^{\prime }&=\left (-\ln \left (y\right )+x^{2}\right ) y \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.515 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{-x^{2}} x}{y \,{\mathrm e}^{x^{2}}+1} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
8.679 |
|
| \begin{align*}
y^{\prime }&=-\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right ) y \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✓ |
✓ |
✗ |
19.325 |
|
| \begin{align*}
y^{\prime }&=\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right )^{2} y \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
20.517 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )+1} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
24.133 |
|
| \begin{align*}
y^{\prime }&=\frac {1+2 \sqrt {4 x^{2} y+1}\, x^{4}}{2 x^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
75.387 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-y^{2}+4 a x \right )^{2}}{y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✓ |
10.110 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (-2+3 x \sqrt {x^{2}+3 y}\right )}{3} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
22.090 |
|
| \begin{align*}
y^{\prime }&=-\frac {x^{2} \left (a x -2 \sqrt {a \left (x^{4} a +8 y\right )}\right )}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
164.442 |
|
| \begin{align*}
y^{\prime }&=\left (-\ln \left (y\right )+x \right ) y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.358 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+x^{2}+2 \sqrt {x^{3}-6 y}}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
9.108 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (a y^{2}+b \,x^{2}\right )^{2} x}{a^{{5}/{2}} y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
25.193 |
|
| \begin{align*}
y^{\prime }&=-\frac {x^{3} \left (\sqrt {a}\, x +\sqrt {a}-2 \sqrt {x^{4} a +8 y}\right ) \sqrt {a}}{2 \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
48.131 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+x \sqrt {x^{2}-2 x +1+8 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
22.504 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}-\frac {a}{2}+x \sqrt {x^{2}+2 a x +a^{2}+4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
13.002 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (\ln \left (y\right )+x^{2}\right ) y}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.721 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a +x \sqrt {-y^{2}+4 a x}}{y} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
63.836 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+1+x \sqrt {x^{2}-4 x +4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
11.974 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 x^{2}+2 x -3 \sqrt {x^{2}+3 y}}{3 \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
8.471 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3} {\mathrm e}^{-\frac {4 x}{3}}}{y \,{\mathrm e}^{-\frac {2 x}{3}}+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
14.402 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (\ln \left (y\right )+x^{3}\right ) y}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.049 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+x^{2} \sqrt {x^{2}-2 x +1+8 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
13.012 |
|
| \begin{align*}
y^{\prime }&=-\frac {x^{2}-1-4 \sqrt {x^{2}-2 x +1+8 y}}{4 \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.994 |
|
| \begin{align*}
y^{\prime }&=-\frac {a x}{2}-\frac {b}{2}+x \sqrt {a^{2} x^{2}+2 a b x +4 a y+b^{2}-4 c} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
13.086 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}-\frac {a}{2}+x^{2} \sqrt {x^{2}+2 a x +a^{2}+4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
22.684 |
|
| \begin{align*}
y^{\prime }&=-\frac {a x}{2}-\frac {b}{2}+x^{2} \sqrt {a^{2} x^{2}+2 a b x +4 a y+b^{2}-4 c} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
12.906 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2}+\frac {1}{2}+x^{2} \sqrt {x^{2}+2 x +1-4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
21.125 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a +x^{2} \sqrt {-y^{2}+4 a x}}{y} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
63.307 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+1+x^{2} \sqrt {x^{2}-4 x +4 y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
12.091 |
|
| \begin{align*}
y^{\prime }&=-\frac {\left (\sqrt {a}\, x^{4}+\sqrt {a}\, x^{3}-2 \sqrt {x^{4} a +8 y}\right ) \sqrt {a}}{2 \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✓ |
2.221 |
|
| \begin{align*}
y^{\prime }&=\left (-\ln \left (y\right )+1+x^{2}+x^{3}\right ) y \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.437 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3} {\mathrm e}^{-2 b x}}{y \,{\mathrm e}^{-b x}+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
14.963 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3} {\mathrm e}^{-2 x}}{{\mathrm e}^{-x} y+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
13.881 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-2 y^{{3}/{2}}+3 \,{\mathrm e}^{x}\right )^{2} {\mathrm e}^{x}}{4 \sqrt {y}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
10.057 |
|
| \begin{align*}
y^{\prime }&=\frac {i x \left (i-2 \sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y\right )}\right ) y}{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
45.821 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (1+x y^{2}\right )^{2}}{y x^{4}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
11.175 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} \left (3 x +\sqrt {-9 x^{4}+4 y^{3}}\right )}{y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
270.863 |
|
| \begin{align*}
y^{\prime }&=\frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{2}+x^{2}}{2 x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
4.565 |
|
| \begin{align*}
y^{\prime }&=-\frac {x^{2}-x -2-2 \sqrt {x^{2}-4 x +4 y}}{2 \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
8.759 |
|
| \begin{align*}
y^{\prime }&=\frac {y+x^{3} a \,{\mathrm e}^{x}+x^{4} a +a \,x^{3}-x y^{2} {\mathrm e}^{x}-y^{2} x^{2}-x y^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.547 |
|
| \begin{align*}
y^{\prime }&=\frac {x +1+2 x^{6} \sqrt {4 x^{2} y+1}}{2 x^{3} \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
12.654 |
|
| \begin{align*}
y^{\prime }&=\frac {y+x^{3} a \ln \left (x +1\right )+x^{4} a +a \,x^{3}-x y^{2} \ln \left (x +1\right )-y^{2} x^{2}-x y^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.615 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} \left (x +1+2 x \sqrt {x^{3}-6 y}\right )}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
46.255 |
|
| \begin{align*}
y^{\prime }&=\frac {y+x^{3} \ln \left (x \right )+x^{4}+x^{3}+7 x y^{2} \ln \left (x \right )+7 y^{2} x^{2}+7 x y^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.846 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+2 x +1+2 \sqrt {x^{2}+2 x +1-4 y}}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
8.159 |
|
| \begin{align*}
y^{\prime }&=\frac {y+x^{3} b \ln \left (\frac {1}{x}\right )+b \,x^{4}+b \,x^{3}+x a y^{2} \ln \left (\frac {1}{x}\right )+a \,x^{2} y^{2}+a x y^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
9.098 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a}{x \left (-y x +2 a x y^{2}-8 a^{2}\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
5.445 |
|
| \begin{align*}
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} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
13.385 |
|
| \begin{align*}
y^{\prime }&=\frac {y+x^{2} \sqrt {x^{2}+y^{2}}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
16.673 |
|
| \begin{align*}
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} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
8.106 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3} x \,{\mathrm e}^{2 x^{2}}}{y \,{\mathrm e}^{x^{2}}+1} \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
16.757 |
|
| \begin{align*}
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} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
10.943 |
|
| \begin{align*}
y^{\prime }&=\frac {y+{\mathrm e}^{\frac {x +1}{x -1}} x^{3}+{\mathrm e}^{\frac {x +1}{x -1}} x y^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
11.245 |
|
| \begin{align*}
y^{\prime }&=\frac {y x -y-{\mathrm e}^{x +1} x^{3}+{\mathrm e}^{x +1} x y^{2}}{\left (x -1\right ) x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.632 |
|
| \begin{align*}
y^{\prime }&=\frac {-x^{2}+1+4 x^{3} \sqrt {x^{2}-2 x +1+8 y}}{4 x +4} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
15.648 |
|
| \begin{align*}
y^{\prime }&=\frac {-\sin \left (2 y\right )+\cos \left (2 y\right ) x^{3}+x^{3}}{2 x} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
4.628 |
|
| \begin{align*}
y^{\prime }&=\frac {y+x^{3} \sqrt {x^{2}+y^{2}}}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
10.270 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-2 b x}+y^{3} {\mathrm e}^{-3 b x}\right ) {\mathrm e}^{b x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
5.697 |
|
| \begin{align*}
y^{\prime }&=\frac {x +1+2 \sqrt {4 x^{2} y+1}\, x^{3}}{2 x^{3} \left (x +1\right )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
12.990 |
|
| \begin{align*}
y^{\prime }&=\frac {y \ln \left (x -1\right )+x^{4}+x^{3}+y^{2} x^{2}+x y^{2}}{\ln \left (x -1\right ) x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.530 |
|
| \begin{align*}
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} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.965 |
|
| \begin{align*}
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}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
5.489 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-2 x}+y^{3} {\mathrm e}^{-3 x}\right ) {\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
5.219 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (-2 x -2+3 x^{2} \sqrt {x^{2}+3 y}\right )}{3 x +3} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
33.679 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x \left (x y^{2}+1+x \right ) y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.364 |
|
| \begin{align*}
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 \ln \left (x \right ) x^{2}-2 x^{2} y+y^{2} \ln \left (x \right )+y^{2}}{{\mathrm e}^{x}-1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
21.350 |
|
| \begin{align*}
y^{\prime }&=\frac {-{\mathrm e}^{x} y+y x -x^{3} \ln \left (x \right )-x^{3}-x y^{2} \ln \left (x \right )-x y^{2}}{\left (x -{\mathrm e}^{x}\right ) x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.528 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (1-x +y \ln \left (x \right ) x^{2}+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (x -1\right ) x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
10.377 |
|
| \begin{align*}
y^{\prime }&=\frac {x y \ln \left (x \right )-y+2 x^{5} b +2 a \,x^{3} y^{2}}{\left (x \ln \left (x \right )-1\right ) x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
8.773 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (\ln \left (y\right )+x +x^{3}+x^{4}\right ) y}{x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.425 |
|
| \begin{align*}
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} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
72.442 |
|
| \begin{align*}
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} \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✓ |
✓ |
✗ |
74.926 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-y^{2}+4 a x \right )^{3}}{\left (-y^{2}+4 a x -1\right ) y} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
15.337 |
|
| \begin{align*}
y^{\prime }&=\frac {2 a x +2 a +x^{3} \sqrt {-y^{2}+4 a x}}{\left (x +1\right ) y} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
61.694 |
|
| \begin{align*}
y^{\prime }&=-\frac {\left (\ln \left (y\right ) x +\ln \left (y\right )-1\right ) y}{x +1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✓ |
20.509 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+2 x +1+2 x^{3} \sqrt {x^{2}+2 x +1-4 y}}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
26.199 |
|
| \begin{align*}
y^{\prime }&=\frac {-a b y+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 )} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
79.862 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}+y \ln \left (x \right ) x^{2}+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right ) x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
12.053 |
|
| \begin{align*}
y^{\prime }&=\frac {-x^{2}+x +2+2 x^{3} \sqrt {x^{2}-4 x +4 y}}{2 x +2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
16.659 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (x +1\right ) y^{2}} \\
\end{align*} |
[_rational] |
✗ |
✓ |
✓ |
✗ |
132.649 |
|
| \begin{align*}
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 )} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
9.732 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2} {\mathrm e}^{2 x^{2}}+y^{3} {\mathrm e}^{3 x^{2}}\right ) {\mathrm e}^{-x^{2}} x \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
7.575 |
|