Let a curve y=f(x) pass through the point (2,( log_e 2)^2) and have slope (2 y)/(x log_e x) for all positive real value of x. Then the value of f(e)…

Let a curve $\displaystyle y=f(x)$ pass through the point $\displaystyle \left(2,\left(\log _{\mathrm{e}} 2\right)^2\right)$ and have slope $\displaystyle \frac{2 y}{x \log _{\mathrm{e}} x}$ for all positive real value of $\displaystyle x$. Then the value of $\displaystyle f(e)$ is equal to \_\_\_\_.