Laplace II: Steps, Impulses & Convolution · Hard problem

A circuit obeys $y'+y=f(t)$, $y(0)=0$, where $f$ is a triangular pulse: $f(t)=t$ for $0\le t<2$, $f(t)=4-t$ for $2\le t<4$, and $f(t)=0$ for $t\ge4$. Use the Laplace transform to find $y(6)$.