$\displaystyle xy'=y$

I have to find a power series solution to this equation of the form $\displaystyle \sum a_{n}x^{n}$

Then solve the equation directly.

I have worked out by studying the equation that the solution is $\displaystyle nx$ but i can't work out how to obtain that answer.

My working so far is:

$\displaystyle xy'-y=0$

$\displaystyle y'-\frac{y}{x}=0$

$\displaystyle \sum na_{n}x^{n-1} - \frac{1}{x}\sum a_{n}x^{n}=0$

(both of sums go from $\displaystyle n=0$ to $\displaystyle \infty$ I wasn't sure how to write those in LaTex.)

Thanks in advance