Determine whether each of the following functions is a solution of Laplace’s equation u x x + u y y = 0 . (a) u = x 2 + y 2 (b) u = x 2 − y 2 (c) u = x 3 + 3 x y 2 (d) u = ln x 2 + y 2 (e) u = sin x cosh y + cos x sinh y (f) u = e − x cos y − e − y cos x
Determine whether each of the following functions is a solution of Laplace’s equation u x x + u y y = 0 . (a) u = x 2 + y 2 (b) u = x 2 − y 2 (c) u = x 3 + 3 x y 2 (d) u = ln x 2 + y 2 (e) u = sin x cosh y + cos x sinh y (f) u = e − x cos y − e − y cos x
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