The Wronskian & Variation of Parameters · Hard problem

An undamped spring obeys $y''+4y=f(t)$ with $y(0)=0$, $y'(0)=0$, where $f(t)=t$ for $0\le t\le\dfrac{\pi}{2}$ and $f(t)=0$ for $t>\dfrac{\pi}{2}$. Find $y(\pi)$.