how to Prove that u(x y)=xy+x-y is a harmonic function and find its harmonic conjugate v(x y)

Question : Prove that u(x y)=xy+x-y is a harmonic function and find its harmonic conjugate v(x y) Solution : Given the function u(x, y) = xy+x-y Differentiating partially we get \[\frac{\partial u}{\partial x}\ \ =\ y+\ 1,\ \frac{\partial u}{\partial y}\…

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