# Math Help - Separation of variables in polar coordinates - Question

1. ## Separation of variables in polar coordinates - Question

Hey guys, Im stuck on the question below. I know how to go about things if the RHS is 0, but with the sine on the RHS Im not sure what to do.

Cheers guys.

2. Using there hint seek a solution in the form

$
u(r,\theta) = \sum_{n=1}^{\infty} R_n(r)\sin 2 n \theta
$
.

When you sub in your PDE you obtain

$
\sum_{n=1}^{\infty} \left( R_n'' + \frac{R_n'}{r} - \frac{4n^2 R_n}{r^2}\right) \sin 2 n \theta = r \sin 2 \theta.
$

Now start indexing n and compare LHS to RHS. You'll get a set of ODEs for $R_n$.

3. Thanks a lot!!

Much appreciated.