2.632   ODE No. 632

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

$$y^{\prime }(x)=\frac{e^x}{e^{-x}y(x)+1}$$ ✓ Mathematica : cpu = 0.142397 (sec), leaf count = 65

$$\text{Solve}[\frac{1}{2}\log (-e^{-2x}y(x{)}^2-e^{-x}y(x)+1)+x=\frac{{\tanh }^{-1}\left(\frac{y(x)+3e^x}{\sqrt{5}(y(x)+e^x)}\right)}{\sqrt{5}}+c_1,y(x)]$$ ✓ Maple : cpu = 1.093 (sec), leaf count = 54

$$\{x-\frac{\sqrt{5}}{5}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}(\frac{2y\left(x\right)\sqrt{5}{\mathrm{e}}^{-x}}{5}+\frac{\sqrt{5}}{5})+\frac{\ln ({\left(y\left(x\right)\right)}^2{\left({\mathrm{e}}^{-x}\right)}^2+y\left(x\right){\mathrm{e}}^{-x}-1)}{2}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$