Power Series Solution for $e^xy''+xy=0$ $$e^xy''+xy=0$$
How do I find the power series solution to this equation, or rather, how should I go about dealing with the $e^x$? Thanks!

Hint:
Expand $$y(x)=\sum\limits_{n=0}^{\infty}{a_n x^n}, \\
e^x=\sum\limits_{n=0}^{\infty}{\dfrac{x^n}{n!}}$$
and substitute them into equation.
