3.773   ODE No. 773

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{xy\left(x\right)+x+{\left(y\left(x\right)\right)}^2}{(x-1)(y\left(x\right)+x)}=0}}$$

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

Mathematica: cpu = 0.053007 (sec), leaf count = 61 $$\text{Solve}[\frac{1}{2}\log (\frac{y(x{)}^2}{x^2}+\frac{y(x)}{x}+1)+\frac{{\tan }^{-1}\left(\frac{\frac{2y(x)}{x}+1}{\sqrt{3}}\right)}{\sqrt{3}}=c_1+\log (1-x)-\log (x),y(x)]$$

Maple: cpu = 0.218 (sec), leaf count = 48 $$\{y\left(x\right)=\frac{\sqrt{3}x}{2}\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\sqrt{3}\ln \left(\frac{3x^2({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+1)}{4{(x-1)}^2}\right)+2\sqrt{3}\mathit{\_}\mathit{C}\mathit{1}-2\mathit{\_}\mathit{Z})\right)-\frac{x}{2}\}$$