Verify that the function u (x, y) = ln (x 2 + y 2 ) +

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Verify that the function u (x, y) = α ln (x2 + y2) + b satisfies Laplace’s equation (3) and determine α and b so that u satisfies the boundary conditions u = 110 on the circle x2 + y2 = 1 and u = 0 on the circle x2 + y2 = 100.

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