SOLVED: 1. Solve Poisson's equation, uxx uyy = f(x,y), (or Laplace's equation if f(x,y) = 0) using the method of eigenfunction expansion for the given boundary conditions.(a) f(x,y) = 0, u(0,y) = u(T,y) = 0, u(x,0) = 1, uy(x,1) = sin(x)(b) f(x,y) = 0, u(0,y) = u(1,y) = 0, u(x,0) uy(x,0) = 0, and uy(x,T) = 0(c) f(x,y) = x, u(0,y) = u(y) = 0, uy(x,0) = 0, uy(x,1) - u(x,1) = 1.2. Plot all solutions and discuss the behaviors of the solutions. Compare them with your solutions above.3. Discuss how
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