3.341   ODE No. 341

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

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

Mathematica: cpu = 0.049506 (sec), leaf count = 33 $$\left\{\{y(x)\to c_1{e}^{-x}-W\left(x{e}^{c_1{e}^{-x}-x}\right)\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 30 $$\{y\left(x\right)=-\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(\frac{x}{{\mathrm{e}}^x}{\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\mathrm{e}}^x}}\right)}^{-1}\right)-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\mathrm{e}}^x}\}$$