2.655   ODE No. 655

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

$$y^{\prime }(x)=\frac{e^{-4x/3}y(x{)}^3}{e^{-2x/3}y(x)+1}$$ ✓ Mathematica : cpu = 15.3076 (sec), leaf count = 82

$$\text{Solve}[\frac{3}{2}\log (y(x))+\frac{1}{28}(-21\log (-3y(x{)}^2+2e^{2x/3}y(x)+2e^{4x/3})+6\sqrt{7}{\tanh }^{-1}\left(\frac{y(x)+2e^{2x/3}}{\sqrt{7}y(x)}\right)+28x)=c_1,y(x)]$$ ✓ Maple : cpu = 2.632 (sec), leaf count = 66

$$\{x+\frac{3\sqrt{7}}{14}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}(\frac{3y\left(x\right)\sqrt{7}}{7}{\mathrm{e}}^{-\frac{2x}{3}}-\frac{\sqrt{7}}{7})-\frac{3}{4}\ln (3{\left(y\left(x\right)\right)}^2{\left({\mathrm{e}}^{-2/3x}\right)}^2-2y\left(x\right){\mathrm{e}}^{-2/3x}-2)+\frac{3}{2}\ln \left(y\left(x\right){\mathrm{e}}^{-\frac{2x}{3}}\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$