Vibrational analysis of carbon nanotubes conveying fluid

Hello everyone!

I really need the community's help.

I am working a project where I am to solve the model equation attached using the boundary conditions to find w(x,t)

I am just looking for the code that can actually generate the defelction w(x,t) after soving and applying the boundary conditions. The values of the constants are liable to change, so therfore are not relevant to this cause. Any arbitary value can be used.

I just need a written code that can aid me to solve the PDE problem presented and I can take it from there myself.

Thank you all very much!