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Find the solution formula for the heat equation ut = c2 uxx on the half-infinite bar...

Find the solution formula for the heat equation ut = c2 uxx on the half-infinite bar (0 ≤ x < ∞) with Dirichlet boundary condition u(0, t) = a, for some constant a, and initial condition u(x, 0) = f(x) using the Fourier sine transform.

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