Laplace Transforms · Challenge problem

Let $y(t)$ solve $t\,y'' + (1 - t)\,y' + 2y = 0$ with $y(0) = 1$, and suppose $y$ has a Laplace transform $Y(s)$ with $sY(s) \to 1$ as $s \to \infty$. Use the Laplace transform to find $y(6)$.