3.343   ODE No. 343

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

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

Mathematica: cpu = 0.037505 (sec), leaf count = 35 $$\text{Solve}[x=c_1{e}^{y(x)}+e^{y(x)}(\text{Ei}(-y(x))-e^{-y(x)}\log (y(x))),y(x)]$$

Maple: cpu = 0.046 (sec), leaf count = 27 $$\{y\left(x\right)={\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\mathit{\_}\mathit{Z}-x-\mathit{E}\mathit{i}(1,{\mathrm{e}}^{\mathit{\_}\mathit{Z}}){\mathrm{e}}^{{\mathrm{e}}^{\mathit{\_}\mathit{Z}}}+{\mathrm{e}}^{{\mathrm{e}}^{\mathit{\_}\mathit{Z}}}\mathit{\_}\mathit{C}\mathit{1})}\}$$