Sorry about the format, bit I have no knowledge of LateX.
A,B - are real constants
U=(Ux,Uy,Uz)
I have a system of three coupled linear second order differential equations
(di)^2(Ui) +A*Laplacian(Ui)+ B*di[Divergence(U)]
Note: The first term is not a sum.
0<z<H, while x & y can...