Laplace Equation Solution?

Hi,

If the Laplace Equation is given as : d^2T/dx^2 + d^2T/dy^2 = 0

and that the solution of T(x,y) must satisfy the equation: e.g T = 2x +1, differentiating it twice wrt x and y would make the solution valid.

Then now if, d^2(k^1/2)/dx^2 + d^2(k^1/2)/dy^2 = 0

and T(x,y) = (k(x,y))^p*phi(x,y) ; T = k^p*phi

how do i determine the value of p so that phi satisfies the laplace equation?