Consider the Laplace equation #xx + Hyy = 0, 0

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Consider The Laplace Equation Xx Hyy 0 0 X 2 0 Y 3 Uy X 0 Y X 3 0 Uz 0 Y 0 4 2 Y H Y Let U X 1 (28.82 KiB) Viewed 90 times

Consider the Laplace equation #xx + Hyy = 0, 0<x< 2, 0 < y < 3 uy(x,0) = y(x, 3) = 0 uz (0,y) = 0, 4,(2,y) =h(y) Let u(x,y) = F(x)G(y) answer I and II (Hint: The eigenvalues and eigenfunctions of the SLP y" + ay = 0, y'(0) = 0, y'(L) = 0 are An = () and yo = cos ("E"), n E (0,1,2,3...) MI F.(x) = A) cosh B) cos C) sin D) sinh) E) None nolill [TI] If u(x,y) = +91:A (EC) GC) Then A, is equal A) A, L'h(y) cos (15) dy B) A. 51 ) Sh(y) cos (CY) dy D) A. = h(y) cos(7Y) dy C) A = 2 sinh E) None