Question: The Laplace operator is defined by = xx + yy . A function u(x, y) satisfying the Laplace equation u =

The Laplace operator Δ is defined by Δƒ = ƒxx + ƒyy. A function u(x, y) satisfying the Laplace equation Δu = 0 is called harmonic.

Find all harmonic polynomials u(x, y) of degree 3, that is, u(x, y) = ax + bxy + cxy + dy.

u(x, y) = ax + bxy + cxy + dy.

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