2.668   ODE No. 668

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

$$y^{\prime }(x)=\frac{e^{-2x}y(x{)}^3}{e^{-x}y(x)+1}$$ ✓ Mathematica : cpu = 0.505397 (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 = 0.693 (sec), leaf count = 58

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