Question

Use the eigenfunction expansion to solve utt = uxx + e −t sin(3x), 0 < x...

Use the eigenfunction expansion to solve utt = uxx + e −t sin(3x), 0 < x < π u(x, 0) = sin(x), ut(x, 0) = 0 u(0, t) = 1, u(π, t) = 0.

Your solution should be in the form of Fourier series. Write down the formulas that determine the coefficients in the Fourier series but do not evaluate the integrals

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Answer #1

The solution of the given non-homogeneous initial-boundary value problem is

where

That is

The method and explanation are given below in detail.

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