3.824   ODE No. 824

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{y\left(x\right)(x^3+x^{2}y\left(x\right)+{\left(y\left(x\right)\right)}^2)}{x^2(x-1)(y\left(x\right)+x)}=0}}$$

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

Mathematica: cpu = 0.055007 (sec), leaf count = 68 $$\text{Solve}[-\frac{1}{2}\log (\frac{y(x{)}^2}{x^2}+\frac{y(x)}{x}+1)+\log \left(\frac{y(x)}{x}\right)+\frac{{\tan }^{-1}\left(\frac{\frac{2y(x)}{x}+1}{\sqrt{3}}\right)}{\sqrt{3}}=c_1+\log (1-x)-\log (x),y(x)]$$

Maple: cpu = 0.280 (sec), leaf count = 61 $$\{\ln \left(\frac{y\left(x\right)}{x}\right)-\frac{1}{2}\ln \left(\frac{{\left(y\left(x\right)\right)}^2+xy\left(x\right)+x^2}{x^2}\right)+\frac{\sqrt{3}}{3}\arctan \left(\frac{(x+2y\left(x\right))\sqrt{3}}{3x}\right)+\ln \left(x\right)-\ln (x-1)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$