Question: Please provide clear, correct solution. Thanks! Let u(;r,t) = X(:r]T(t], i.e. u is separable. Then, show that: E E)u(:r,t) _ 8U(5c,s) 3:1: (3:1: where U[:::,s)

Please provide clear, correct solution. Thanks!

Let u(;r,t) = X(:r]T(t], i.e. u is separable. Then, show that: E E)u(:r,t) _ 8U(5c,s) 3:1: (3:1: where U[:::,s) = X(:I:JS(S), 3(3) = {T(}}. Then, show the same for: ,C 3\"1:.(m}) _5"U[:i:,s} BIN. _ 3113" where n represents all positive integers

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