Laplace II: Steps, Impulses & Convolution · Challenge problem

An RC circuit obeys $y'+y=f(t)$, $y(0)=0$, where the input ramps up and then holds: $f(t)=t$ for $0\le t<1$ and $f(t)=1$ for $t\ge1$. Use the Laplace transform to find $y(2)$. Give an exact answer.