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Show that the function satisfies the two-dimensional Laplace's equation $u_{x x}+u_{y y}=0 .$ $$u=e^{-x} \cos y+e^{-y} \cos x$$...

Question

Show that the function satisfies the two-dimensional Laplace's equation $u_{x x}+u_{y y}=0 .$ $$u=e^{-x} \cos y+e^{-y} \cos x$$

Show that the function satisfies the two-dimensional Laplace's equation $u_{x x}+u_{y y}=0 .$ $$u=e^{-x} \cos y+e^{-y} \cos x$$

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