Assumed solution for the Laplace EQUATION?? The book I'm using says that the method of separation of variables is a must when solving the Laplace equation. OK, well they ASSUME that the solution looks like V(x,y,z) = X(x)*Y(y)*Z(z) but why can't they assume a solution of V(x,y,z) = X(x) + Y(y) + Z(z) ????? When performing the [itex]\nabla \bullet [/itex]([itex]\nabla[/itex]V) operation, the difference is that their assumed solution leads to [1/X(x)]* d2[X(x)]/dx2 = -kx2, while what I'm proposing will lead to just d2[X(x)]/dx2 = -kx2 Since what I'm proposing is easier, why would that be the one used? Thanks.