(Laplace Transforms) (a) Use the definition of the Laplace transform to compute L{cosh(at)}, where a E R\{0}. What's the domain of L{cosh(at)}? (b) Use Laplace transforms to solve y" – a?y = cosh(at) where y(b) be R. = 1 and y'(b) = 2 and (c) Is the solution in part (b) unique? Justify using a theorem. (d) Solve the IVP in part (b) again using a different method. Must both solutions be the same? Why or why not? If so, show that they are equivalent.

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