2.689   ODE No. 689

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

$$y^{\prime }(x)=\frac{-e^{x+1}{x}^3+e^{x+1}xy(x{)}^2+xy(x)-y(x)}{(x-1)x}$$ ✓ Mathematica : cpu = 0.06607 (sec), leaf count = 60

$$\left\{\{y(x)\to -\frac{x(e^{2c_1+2e^2\text{Ei}(x-1)+2e^{x+1}}-1)}{e^{2c_1+2e^2\text{Ei}(x-1)+2e^{x+1}}+1}\}\right\}$$

✓ Maple : cpu = 0.044 (sec), leaf count = 25

$$\{y\left(x\right)=-\tanh ({\mathrm{e}}^{1+x}-{\mathrm{e}}^2\mathit{E}\mathit{i}(1,1-x)+\mathit{\_}\mathit{C}\mathit{1})x\}$$