If the solution curve f(x, y)=0 of the differential equation (1+ log_e x) (d x)/(d y)-x log_e x=e^y, x>0, passes through the points (1,0) and (α, 2),…

If the solution curve $\displaystyle f(x, y)=0$ of the differential equation $\displaystyle \left(1+\log _e x\right) \frac{d x}{d y}-x \log _e x=e^y, x>0$, passes through the points $\displaystyle (1,0)$ and $\displaystyle (\alpha, 2)$, then $\displaystyle \alpha^\alpha$ is equal to