For which values of a, b and c is the function harmonic? Explain your answer. (b)...

 

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For which values of a, b and c is the function harmonic? Explain your answer. (b) [15p] Using the mean value property, u(x, y) = ax³ + bxy² + cy for the boundary value problem Uxx + Uyy = 0, (x, y) = B u(x, y) = 1 + xy, (x, y) є дв evaluate u(0, 0) where B = {(x, y) = R² | x² + y² <4}. For which values of a, b and c is the function harmonic? Explain your answer. (b) [15p] Using the mean value property, u(x, y) = ax³ + bxy² + cy for the boundary value problem Uxx + Uyy = 0, (x, y) = B u(x, y) = 1 + xy, (x, y) є дв evaluate u(0, 0) where B = {(x, y) = R² | x² + y² <4}.