Question: Use the eigenfunction expansion to solve the non-homogeneous PDE: I Utt = kuxx + ter, 0 0 u(t, 0) = 0, u(t, L) = 0,

Use the eigenfunction expansion to solve the non-homogeneous PDE: I Utt = kuxx + ter, 0 0 u(t, 0) = 0, u(t, L) = 0, u(0, 20) = 2, ut ( 0 , z ) = 0 , Assume k > 0. Note that the eigenfunctions for the non-homogeneous version of the PDE are given by On = sin(" x), for n > 0, where n E N. Write your solution u(t, x)

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