Laplace Transforms · Superchallenge problem

A first-order filter $y' + y = f(t)$ is driven by the square wave of period $2$ with $f(t) = 1$ for $0 \le t < 1$ and $f(t) = 0$ for $1 \le t < 2$, repeated. Using the Laplace transform, find the initial value $y(0)$ for which the solution is itself periodic with period $2$.