2.166   ODE No. 166

1. Problem in Latex
2. Mathematica input
3. Maple input

$$2(x-1)x{y}^{\prime }(x)+(x-1)y(x{)}^2-x=0$$ ✓ Mathematica : cpu = 0.13584 (sec), leaf count = 71

$$\left\{\{y(x)\to \frac{2x(-G_{2,2}^{2,0}\left(x|\begin{array}{c}-\frac{1}{2},\frac{1}{2}\\ -1,0\end{array}\right)+\frac{c_1(E(x)-K(x))}{\pi x})}{G_{2,2}^{2,0}\left(x|\begin{array}{c}\frac{1}{2},\frac{3}{2}\\ 0,0\end{array}\right)+\frac{2c_{1}E(x)}{\pi }}\}\right\}$$ ✓ Maple : cpu = 0.112 (sec), leaf count = 97

$$\{y\left(x\right)=\frac{x}{2x-2}(\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(-\frac{1}{2},1,\frac{2-x}{x})\mathit{\_}\mathit{C}\mathit{1}-\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(\frac{1}{2},1,\frac{2-x}{x})\mathit{\_}\mathit{C}\mathit{1}+\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{P}(-\frac{1}{2},1,\frac{2-x}{x})-\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{P}(\frac{1}{2},1,\frac{2-x}{x})){(\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(-\frac{1}{2},1,\frac{2-x}{x})\mathit{\_}\mathit{C}\mathit{1}+\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{P}(-\frac{1}{2},1,\frac{2-x}{x}))}^{-1}\}$$