Series solution to first order differential equation I need to find a series solution to the following simple differential equation
$$x^2y'=y$$
Assuming the solution to be of the form $y=\sum a_nx^n$  and equating the coefficients on both the sides, all the coefficients turn out to be zero which is definitely wrong.
Please guide me to the correct solution.
Any help is appreciated. Thanks!

Well,
\begin{eqnarray}
\int \frac{dy}{y} &=& \int \frac{dx}{x^{2}}\\
\implies \ln y    &=& -\frac{1}{x}+c
\end{eqnarray}
Hence,
\begin{equation}
y=Ae^{-\frac{1}{x}}
\end{equation}
Is a series solution necessary?
