Find the general solution of the differential equation $$x^2y'' + xy' + (2 x^2-16) y = 0 \;.$$
Answer: $\displaystyle y = c \sum_{n=m}^\infty c_n x^n \;,$
where
$\qquad c_n =$ if $n\ge m$ and $n=2k$ is even,
$\qquad c_n =$ if $n\ge m$ and $n=2k+1$ is odd,
$m =$ , and $c$ is an arbitrary constant.

Choose your answer so that $c_m = 1$.

Note: Because the coefficient of $y''$ is zero when $x=0$, you will not find two linearly independent solutions of the differential equation defined near $x=0$. In fact, by looking at the differential equation, you can see that any solution defined on an open interval containing $x=0$ must have $y(0)=0$.