I'm trying to solve the following differential equation with non constant coefficients:

$\displaystyle 2xy'' + y' + xy = 0$

I'm totally confused about finding the recurrence relation when solving this when using the method of Frobenius about $\displaystyle x_0 = 0$. I know it's a regular singular point and all that but I'm just rubbish at finding the recurrence relation, apparently the right answer is

$\displaystyle a_n = - \frac{a_{n-2}}{(n+r)(2(n+r) -1)} $where r is one of the roots of the indicial equation

Can anyone help me get unconfused about finding the recurrence relation as I'm rubbish at it.