# Solving a PDE system

I have the following system of second order linear PDEs.

## 6) $$Q_{2} = \frac{\partial M_{2}}{\partial y} - \frac{\partial M_{3}}{\partial x}$$

with all of the $$w$$, $$M_{1}$$, $$M_{2}$$, $$M_{3}$$, $$Q_{1}$$, $$Q_{2}$$ being functions of $$(x, y)$$ of course and all the $$C_i$$s known and constant.

I am not posting the boundary conditions as I am not looking for a complete solution of the above, but I would like some guidance regarding how to approach it. Any help\hint would be highly appreciated.

More specifically, I am interested in knowing how one would go about implementing a numerical method.

For some background info in case that is in any way helpful\interesting, the problem has to do with the buckling of composite plates.

• @hardmath I hope the edit helps clear the question. – Ev. Kounis Oct 2 '18 at 7:16
• Thanks for the clarification. The application to buckling of a composite plate would suggest the use of finite element discretization, and it would be helpful to know the region over which the PDEs are to hold. – hardmath Oct 3 '18 at 16:33