The Wronskian & Variation of Parameters · Challenge problem

Solve the third-order equation $y^{\prime\prime\prime}+y'=\tan t$ on $-\dfrac{\pi}{2}<t<\dfrac{\pi}{2}$ with $y(0)=y'(0)=y''(0)=0$, and give $y\!\left(\dfrac{\pi}{4}\right)$.