Frobenius & Special Functions · Challenge problem

The equation $x^2y'' + 5xy' + 13y = 0$ (for $x>0$) has complex indicial roots $-2 \pm 3i$. The solution with $y(1) = 0$, $y'(1) = 2$ is zero at $x=1$. Find the next value of $x > 1$ where it is zero again. Give an exact answer.