Incompressible Navier-Stokes Problem

I am stuck on this problem:

Incompressible N-S

Incompressible,

Pressure is uniform with

Show that

with general solution

Choose A and B to satisfy the no-slip because at r = a, r = b. Derive

__________________________________________________ _________

Since posting this I have gotten farther, solving the differential equation as a linear nonhomogenious equation I get

meaning

plugging w back into the differential equation I get

this equation does satisfy the differential equation but as far as matching the equation for w above I dont understand how they are getting the term.