Find the fundamental set of solutions to the equation
$$xy'' + y' + y = 0$$
Express the functions in terms of power series.
I have found the general solution to be
$$a_{n+1} = \frac{-a_{n}} { (n + 1)^2}$$
However, I am having trouble finding the fundamental set of solutions. Thank you.
$$ \frac{a_n}{a_0}=\prod_{k=0}^{n-1}{\frac{a_{k+1}}{a_k}}=(-1)^n\prod_{k=0}^{n-1}{\frac{1}{(k+1)^2}}=(-1)^n\frac{1}{(n!)^2}$$