Laplace II: Steps, Impulses & Convolution · Challenge problem

An overdamped system at rest, $y''+3y'+2y=f(t)$ with $y(0)=y'(0)=0$, receives the input $f(t)=e^{-t}u(t-1)$ (a decaying signal that is switched on at $t=1$). Find $y(2)$. Give an exact answer.