Solving this Laplacian Equation?

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How do I solve the following?

$\frac{∂^2\phi}{∂x^2}$ + $\frac{∂^2\phi}{∂y^2}$ + $\lambda^2\phi$ = $0$

To start of with, is it right to consider using the method of separation of variables, or is there another way to start tackling this problem.