If the curve y=f(x) passes through the point ( 1, e ) and satisfies the differential equation d y=y(2+ log_e x) d x, x>0, then f( e ) is equal to:

If the curve $\displaystyle y=f(x)$ passes through the point ( $\displaystyle 1, \mathrm{e}$ ) and satisfies the differential equation $\displaystyle \mathrm{d} y=y\left(2+\log _{\mathrm{e}} x\right) \mathrm{d} x, x>0$, then $\displaystyle f(\mathrm{e})$ is equal to :