3.213   ODE No. 213

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

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

Mathematica: cpu = 0.100513 (sec), leaf count = 71 $$\text{Solve}[\frac{1}{2}\log \left(\frac{x^2-y(x{)}^2+(x-3)y(x)-x-1}{(x-1{)}^2}\right)+\log (1-x)=c_1+\frac{{\tanh }^{-1}\left(\frac{y(x)+2x-1}{\sqrt{5}(y(x)+1)}\right)}{\sqrt{5}},y(x)]$$

Maple: cpu = 0.624 (sec), leaf count = 73 $$\{-\frac{1}{2}\ln (-\frac{{(x-1)}^2-(x-1)(-y\left(x\right)-1)-{(-y\left(x\right)-1)}^2}{{(x-1)}^2})-\frac{\sqrt{5}}{5}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\frac{(x-3-2y\left(x\right))\sqrt{5}}{5x-5}\right)-\ln (x-1)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$