Laplace Transforms · Superchallenge problem

Use the Laplace transform to solve $y'' + 2t\,y' - 4y = 1$, $y(0) = 0$, $y'(0) = 0$, and find $y(4)$. (Assume $y$ has a Laplace transform $Y(s)$ with $Y(s) \to 0$ as $s \to \infty$.)