The Wronskian & Variation of Parameters · Hard problem

One solution of $ty''+2y'+ty=0$ on $t>0$ is $y_1=\dfrac{\sin t}{t}$. Find the solution with $y\!\left(\dfrac{\pi}{2}\right)=0$ and $y'\!\left(\dfrac{\pi}{2}\right)=-\dfrac{2}{\pi}$, and give $y(\pi)$.