Question: - 4) Consider the initial value problem Ou = dzu+F(x, t), I, LER, u(x, 0) = f(I), du(x, 0) = g(x). Assume that f, g

- 4) Consider the initial value problem Ou = dzu+F(x, t), I, LER, u(x, 0) = f(I), du(x, 0) = g(x). Assume that f, g are odd (even) functions, and for any te R, F(, t) is an odd (even) function in re K. Using the uniqueness of the solution of the above problem, prove that for any te R u(c, t) is an odd (even) function of r E R

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