(Solved): The (2-dimensional) Laplace operator is defined by u=uxx+uyy. A fu ...

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The (2-dimensional) Laplace operator $$?$$ is defined by $$?u=u_{xx}+u_{yy}.$$ A function $$u$$ is said to be harmonic if it satisfies to Laplace equation (arises in the study of heat transfer, fluid flow, electrostatics, etc.) $$?u=0.$$ Find all constants $$m,n?\mathbb{R}$$ such that $$u(x,y)=\cos (mx)e^{ny}$$ is harmonic.