2. Laplace transforms for integro-differential equations: Consider the equation i(t) + ax(t) + [*g(t − u)x(u) du = f(t); x(0) = 0, for some constant a and functions f and g. (a) Determine an expression for the Laplace transform of a in terms of the Laplace transforms f(s) and g(s) of f and g. (b) Find r(t) in the case when a = 0, f(t) = et and g(t) = 1.

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