Laplace II: Steps, Impulses & Convolution · Challenge problem

A damped system with fading memory obeys $y'(t)=-\displaystyle\int_0^t e^{-2(t-\tau)}\,y(\tau)\,d\tau$ with $y(0)=1$: the restoring force depends on past values, weighted less the older they are. Use the Laplace transform to find $y(1)$.