Question: Problem 3. (30 points): D'Alembert Solution of the Wave Equation Verify that the following function 1 ratct u(x, t) = uo(x - ct) + uo(x

Problem 3. (30 points): D'Alembert Solution of the Wave Equation Verify that the following function 1 ratct u(x, t) = uo(x - ct) + uo(x + ct) + vo( s) ds 2 2c Jx-ct is a solution to the wave equation Utt - Curr= 0, t> 0, x E (0, L) u(0, t) = 0, u(L, t)= 0 u(x, 0) = uo(x), ut(x, 0)= vo(2). (Note that both uo(x) and vo(x) are Odd functions. Then what is / vo(s) ds). (HINT: Make sure to verify that the given solution satisfy the PDE and all the initial-boundary con- ditions

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