PDEs/ODEs using polar coordinates

http://i40.tinypic.com/o6xlps.png

I've got the solutions up to g(Ɵ). But my lecturer then works out for f(r).

We worked out the alpha value and to this part I understand that it is alpha=sqrt mu squared, but since mu is n (from earlier proven that g theta has to be periodic hence mu=n), so alpha is +- n.

What I dont understand is how my lecturer found out that by finding alpha,

the solution to f(r) is:

f(r)=Cr^n + D r^-n if n not equals to zero

and I dont understand how to work it out for n=0 case.