If the solution curve y=f(x) of the differential equation (x^2-4) y^′-2 x y+2 x(4-x^2)^2=0, x>2, passes through the point (3,15), then the local…

If the solution curve $\displaystyle y=f(x)$ of the differential equation $\displaystyle \left(x^2-4\right) y^{\prime}-2 x y+2 x\left(4-x^2\right)^2=0, x>2$, passes through the point $\displaystyle (3,15)$, then the local maximum value of $\displaystyle f$ is $\displaystyle \_\_\_\_$