I'm solving the velocity profile of a fluid flow and am having trouble figuring out how to approach the solution to the partial differential equation below for u(r,t).
$$ \frac{\partial u}{\partial t} - \frac{\Delta p}{\rho L} e^{-i\omega t} = \mu \left(\frac{\partial ^2}{\partial r^2} + \frac{1}{r}\frac{\partial}{\partial r}\right)u $$
I know if the $\frac{\Delta p}{\rho L} e^{-i\omega t}$ term wasn't there I could use separation of variables, but I'm not sure how to get around that added term.