Question: Analytical Solution to Fourth Order Partial Differential Equation

Hi All,

Given the partial differential equation of a plate on an elastic foundation, how do I solve the analytical solution for the deflection given the boundary conditions.

This is what I have:

partial differential equation of a plate on an elastic foundation:
> pde := E*(diff(w(r, phi), r, r, r, r)+2*(diff(w(r, phi), r, r, phi, phi))+diff(w(r, phi), phi, phi, phi, phi))+k*w(r, phi) = 0

The solution for w(r, phi) of this is:
solution := pdsolve(pde, {w(r, phi)})

Then I do the following:
simplify(pdsolve(pde, INTEGRATE, build), size) assuming 0 <= phi, phi <= PI, r > R

Now I need to know the constants given in the analytical solution for w(r, phi). How do I do this?

I tried this:
simplify(pdsolve(pde, boundarycond2, type = numeric), size)  assuming 0 <= phi, phi <= PI, r > R

But I get the following error:
Error, (in assuming) when calling '`pdsolve/numeric/process_IBCs`'. Received: 'initial/boundary conditions must depend upon exactly one of the independent variables: limit(w(r, phi), r = infinity) = 0'
 
Can someone help me out=

Thanks!