3.618   ODE No. 618

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

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

Mathematica: cpu = 0.103513 (sec), leaf count = 25 $$\left\{\{y(x)\to -W(-\frac{e^{c_1{e}^x-1}}{x})-1\}\right\}$$

Maple: cpu = 0.312 (sec), leaf count = 34 $$\{y\left(x\right)=\frac{1}{x}({\mathrm{e}}^{-\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}(-\frac{{\mathrm{e}}^{{\mathrm{e}}^x\mathit{\_}\mathit{C}\mathit{1}-1}}{x})+{\mathrm{e}}^x\mathit{\_}\mathit{C}\mathit{1}-1}-x)\}$$