Laplace Transforms · Superchallenge problem

Let $y(t)$ be the solution of $t\,y'' + y' + t\,y = 0$ that is bounded near $t = 0$ with $y(0) = 1$ (it has a Laplace transform $Y(s)$ for $s > 0$). Without solving for $y$, use the Laplace transform to find $Y\!\left(\dfrac34\right)$.