Frobenius & Special Functions · Medium problem

The equation $2xy'' + 3y' - y = 0$ has indicial roots $0$ and $-\tfrac12$ at $x = 0$. Let $y = \sum_{n\ge0}a_nx^{n - 1/2}$ be the Frobenius solution for the smaller root, with $a_0 = 1$. Compute $a_3$. Express your answer as a common fraction.