Consider the equation (t) + t 0 k(t )() d = f(t), in which f and k are known functions

Chapter 6, Problem 21

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Consider the equation (t) + t 0 k(t )() d = f(t), in which f and k are known functions, and is to be determined. Since the unknown function appears under an integral sign, the given equation is called an integral equation; in particular,it belongs to a class of integral equations known asVolterra integral equations. Take the Laplace transform of the given integral equation and obtain an expression for L{(t)} in terms of the transforms L{f(t)} and L{k(t)} of the given functions f and k. The inverse transform of L{(t)} is the solution of the original integral equation.

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