Verify that each of the functions uo = y, satisfies Laplace's equation (Sec. 23) and the...

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Verify that each of the functions uo = y, satisfies Laplace's equation (Sec. 23) and the boundary conditions Un un = sinh ny cos nx : Uxx (x, y) + Uyy (x, y) = 0 (n = 1,2,...) u(x, y)=Aoy+) A, sinh nycos nx n=1 (0 < x <л, 0< y < 2) ux(0, y) = ux(π, y) = 0, u(x, 0) = 0. Then use the superposition principle in Sec. 33 to show formally, without considering questions of convergence, differentiability, or continuity, that the series Verify that each of the functions uo = y, satisfies Laplace's equation (Sec. 23) and the boundary conditions Un un = sinh ny cos nx : Uxx (x, y) + Uyy (x, y) = 0 (n = 1,2,...) u(x, y)=Aoy+) A, sinh nycos nx n=1 (0 < x <л, 0< y < 2) ux(0, y) = ux(π, y) = 0, u(x, 0) = 0. Then use the superposition principle in Sec. 33 to show formally, without considering questions of convergence, differentiability, or continuity, that the series

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Solution 940 221 Then alt 0 2x Then unn cory 222 Now 52410 coy un Rinhny conn ... View the full answer