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1. Solve fully the heat equation problem: ut = 5uxx u(0, t) = u(1, t) =...

1. Solve fully the heat equation problem: ut = 5uxx u(0, t) = u(1, t) = 0 u(x, 0) = x − x ^3 (Provide all the details of separation of variables as well as the needed Fourier expansions.)

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