Proceed as in this example to solve the given boundary-value problem. a²u au ax? 0 < x < 1, t> 0, at u(0, t) = 1 – e-t, u(1, t) = 1 – e-t, t> 0 u(x, 0) = 0, 0

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A: We simplify f'(t) by expanding  To find f(t) we integrate f'(t) C=integrating constant

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A: Recall the Leibniz rule:

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A: Step 1:   Step 2:To estimate the interval of existence of the solution, we can utilize the theorem's…

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