3.668   ODE No. 668

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{{\left(y\left(x\right)\right)}^3{\mathrm{e}}^{-2x}}{y\left(x\right){\mathrm{e}}^{-x}+1}=0}}$$

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

Mathematica: cpu = 0.536568 (sec), leaf count = 78 $$\text{Solve}[\log (y(x))+y(x{)}^2(\frac{x}{y(x{)}^2}-\frac{\log (-y(x{)}^2+e^{x}y(x)+e^{2x})}{2y(x{)}^2}+\frac{{\tanh }^{-1}\left(\frac{y(x)+2e^x}{\sqrt{5}y(x)}\right)}{\sqrt{5}y(x{)}^2})=c_1,y(x)]$$

Maple: cpu = 0.546 (sec), leaf count = 58 $$\{y\left(x\right)={\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(2\sqrt{5}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(1/5\frac{({\mathrm{e}}^x-2{\mathrm{e}}^{\mathit{\_}\mathit{Z}})\sqrt{5}}{{\mathrm{e}}^x}\right)+5\ln ({\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2-{\mathrm{e}}^{x+\mathit{\_}\mathit{Z}}-{\left({\mathrm{e}}^x\right)}^2)+10\mathit{\_}\mathit{C}\mathit{1}-10\mathit{\_}\mathit{Z}-10x)}\}$$