3.632   ODE No. 632

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

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

Mathematica: cpu = 0.168521 (sec), leaf count = 65 $$\text{Solve}[\frac{1}{2}\log (-e^{-2x}y(x{)}^2-e^{-x}y(x)+1)+x=c_1+\frac{{\tanh }^{-1}\left(\frac{y(x)+3e^x}{\sqrt{5}(y(x)+e^x)}\right)}{\sqrt{5}},y(x)]$$

Maple: cpu = 0.203 (sec), leaf count = 52 $$\{x+\frac{\ln ({\left(y\left(x\right)\right)}^2{\left({\mathrm{e}}^{-x}\right)}^2+y\left(x\right){\mathrm{e}}^{-x}-1)}{2}-\frac{\sqrt{5}}{5}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\frac{(1+2y\left(x\right){\mathrm{e}}^{-x})\sqrt{5}}{5}\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$