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Consider the nonhomogenous heat equation with time dependent sources ut = uxx + xt, an initial...

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Advance Math

Consider the nonhomogenous heat equation with time dependentsources ut = uxx + xt, an initial conditionu(x, 0) = x2 and inhomogenous boundary conditionsux(0, t) = 2t and ux(1, t) = 4. Use eigenfunction expansion to find the solution u(x, t).

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