3.633   ODE No. 633

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

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

Mathematica: cpu = 0.191024 (sec), leaf count = 85 $$\text{Solve}[7(-9c_1+3\log (-\frac{2}{3}{e}^{-4x/3}y(x{)}^2-\frac{2}{3}{e}^{-2x/3}y(x)+1)+4x)=6\sqrt{7}{\tanh }^{-1}\left(\frac{y(x)+4e^{2x/3}}{\sqrt{7}(y(x)+e^{2x/3})}\right),y(x)]$$

Maple: cpu = 0.686 (sec), leaf count = 52 $$\{y\left(x\right)=1\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-343{(\tanh \left(1/6(4\mathit{\_}\mathit{C}\mathit{1}-4x-3\mathit{\_}\mathit{Z})\sqrt{7}\right))}^2+343+98{\mathrm{e}}^{\mathit{\_}\mathit{Z}})}-3+2\mathit{\_}\mathit{Z}+2{\mathit{\_}\mathit{Z}}^2){\left({\mathrm{e}}^{-\frac{2x}{3}}\right)}^{-1}\}$$