3.688   ODE No. 688

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

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

Mathematica: cpu = 0.116515 (sec), leaf count = 78 $$\left\{\{y(x)\to x\tan \left(\frac{1}{2}(2c_1-8e\text{Ei}\left(\frac{2}{x-1}\right)+e^{\frac{x}{x-1}+\frac{1}{x-1}}{x}^2+2e^{\frac{x}{x-1}+\frac{1}{x-1}}x-3e^{\frac{2}{x-1}+1})\right)\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 61 $$\{y\left(x\right)=\tan (\frac{x^2}{2}{\mathrm{e}}^{\frac{1+x}{x-1}}+x{\mathrm{e}}^{\frac{1+x}{x-1}}+4\mathrm{e}\mathit{E}\mathit{i}(1,-2{(x-1)}^{-1})-\frac{3}{2}{\mathrm{e}}^{\frac{1+x}{x-1}}+\mathit{\_}\mathit{C}\mathit{1})x\}$$