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5. Find the solution of the PDE with the prescribed auxiliary conditions by the method of separation variables: (a)ux = uy ; u(0, y) =

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5. Find the solution of the PDE with the prescribed auxiliary conditions by the method of separation variables: (a)ux = uy ; u(0, y) = 2ey. Ans : u (x, y) = 2e3(x+y) (b) Uxx = Utt ; U(0, t) = 0, U(n, t) = 0, U(x, 0) = sin 3 x, U.(x, 0) = 0. (Wave eqn). Ans: U(x, t) = sin 3 x cos3t

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