I am completely lost on solving the following Fourth order Partial Differential Equation involving fourth Power of Del Operator. I am weak in solving PDE in general and this totally gives me a headache. I found in internet that this is of biharmonic type (!!!)
\begin{equation} \nabla^4w + (\frac{NC^2}{D})\nabla^2w = 0, \end{equation} where \begin{equation} \nabla^2= \frac{1}{r^2}\frac{\partial^2}{\partial\theta^2} + \frac{1}{r} \frac{\partial }{\partial r} + \frac{\partial^2}{\partial r^2} , \end{equation}
$N,C$ and $D$ are some constants.
Is there a method to solve this?