3.565   ODE No. 565

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

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

Mathematica: cpu = 0.011501 (sec), leaf count = 25 $$\left\{\{y(x)\to c_1{e}^{\frac{1}{2}W{\left(e^x\right)}^2+W\left(e^x\right)}\}\right\}$$

Maple: cpu = 0.093 (sec), leaf count = 17 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left({\mathrm{e}}^x\right)(\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left({\mathrm{e}}^x\right)+2)}{2}}\}$$