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

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

u(x, 0) = 0

ut(x, 0) = 0.1x(π − x)

u(0,t) = u(π,t) = 0

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

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

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Expert Solution

Colby Messinger answered 1 year ago

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