List of top Ordinary Differential Equations Questions on Power Series

If \( y = \sum_{k=0}^{\infty} a_k x^k \), \( (a_0 \neq 0) \) is the power series solution of the differential equation
\[ \frac{d^2y}{dx^2} - 24x^2y = 0, \text{ then } \frac{a_4}{a_0} = \text{\(\underline{\hspace{2cm}}\).} \]