Frobenius & Special Functions · Hard problem

The equation $xy'' + (3 - x)y' - y = 0$ has indicial roots $0$ and $-2$ at $x = 0$. Let $y = \sum_{n\ge0}a_nx^n$ be the Frobenius solution for $r = 0$ with $a_0 = 1$. Sum the series in closed form and compute $y(2)$.