( 30 points): Solve the following wave equation with boundary and initial conditions by the method of separation of variables: c2uxx?=utt?,0

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( 30 points): Solve the following wave equation with boundary and initial conditions by the method of separation of variables:

c^{2} u_{xx} = u_{tt}, 0 < x < L, 0 < t < ? u (0, t) = 0, u (L, t) = 0, u (x, 0) = 0, u_{t} (x, 0) = \frac{? u}{? t} ? ?_{t = 0} = x (L ? x)

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(Solved): ( 30 points): Solve the following wave equation with boundary and initial conditions by the met ...