. Consider the following problem for Laplaceís equation in a rectangle. @ 2u @x2 (x; y) + @ 2u @y2 (x; y) = 0 for all (x; y) in the rectangle [0; 8] [0; 4] which is all (x; y) where 0 x 8 and 0 y 4 and u(x; y) = F(x; y) for all (x; y) on the boundary of [0; 8] [0; 4] where F(x; y) = x 3 + y 2 + xy + 2 Find the function v of the form v(x; y) = ax + by + cxy + d such that v(x; y) = F(x; y