What is the easiest way to solve the following PDE:
d^u/dx^2 + d^2u/dy^2 = m, where m=constant
BC'S: At y=*/- 3^0.5 x, u=0 & at y=H/2, u is finite
Thank you

I can perhaps suggest one way to solve this.  I think this is
Poisson's equation: div(u) = m with inhomogeneous boundary conditions
u = a(x,y) on boundary.

I'm not exactly sure what the first B.C. is, so maybe I'll just
suggest a general course for now:
You could consider the solution u in two parts: 
u = u_i + u_b with
div(u_i) = m and u_i = 0 on the boundary, and
div(u_b) = 0 and u_b = a(x,y) on the boundary.
(The sum of these two functions u = u_i + u_b satisfies the original
DE and boundary conditions.)

The first equation can be solved using separation of variables, which
wouldn't be too bad except for the funny shape of the domain (would
expect sines and cosines for homogenous BC's on rectangular domain). 
Then the second one can be solved with Green's formula.

I know saying that is a lot easier than actually solving it, but maybe
this might help enough to save the $10....