Show all your work. No points will be given to correct answers without reason- able work....

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Show all your work. No points will be given to correct answers without reason- able work. Question 1. (25pts.) Let D = {(x, y) E R? | 0 < z < 2, 0 < y < 1}. Find the solution of the Laplace's equation u (r, y) + uyy(x, y) = 0 for (x, y) in D subject to the boundary %3D conditions u(0, y) = 3 sin(47y), u(2, y) = 0 for 0 Show all your work. No points will be given to correct answers without reason- able work. Question 1. (25pts.) Let D = {(x, y) E R? | 0 < z < 2, 0 < y < 1}. Find the solution of the Laplace's equation u (r, y) + uyy(x, y) = 0 for (x, y) in D subject to the boundary %3D conditions u(0, y) = 3 sin(47y), u(2, y) = 0 for 0