2.667   ODE No. 667

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

$$y^{\prime }(x)=\frac{e^{-2bx}y(x{)}^3}{e^{-bx}y(x)+1}$$ ✓ Mathematica : cpu = 0.935379 (sec), leaf count = 90

$$\text{Solve}[\frac{\log (y(x))}{b}+\frac{1}{2}(-\frac{\log (y(x{)}^2-b{e}^{bx}(e^{bx}+y(x)))}{b}+\frac{2{\tanh }^{-1}\left(\frac{\sqrt{\frac{b}{b+4}}(2e^{bx}+y(x))}{y(x)}\right)}{\sqrt{b}\sqrt{b+4}}+2x)=c_1,y(x)]$$

✓ Maple : cpu = 0.209 (sec), leaf count = 83

$$\{bx+b\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left((2y\left(x\right){\mathrm{e}}^{-bx}-b)\frac{1}{\sqrt{b^2+4b}}\right)\frac{1}{\sqrt{b^2+4b}}+\ln \left(y\left(x\right){\mathrm{e}}^{-bx}\right)-\frac{\ln (-by\left(x\right){\mathrm{e}}^{-bx}+{\left(y\left(x\right)\right)}^2{\left({\mathrm{e}}^{-bx}\right)}^2-b)}{2}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$