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  3. for the wave equation, utt = c2uxx, with the follo

For the wave equation, utt = c2uxx, with the following boundary and initial conditions, u(x, 0) =...

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Advance Math

For the wave equation, utt = c2uxx, with the following boundaryand initial conditions,

u(x, 0) = 0

ut(x, 0) = 0.1x(π − x)

u(0,t) = u(Ï€,t) = 0

(a) Solve the problem using the separation of variables.

(b) Solve the problem using D’Alembert’s solution. Hint: I wouldsuggest doing an odd expansion of ut(x,0) first; the final solutionshould be exactly like the one in (a).

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