(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" – a²y = cosh(at) where y(b) = 1 and y' (b) = 2 and bE R. (c) Is the solution in part (b) unique? Justify using a theorem.

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Chapter2: Second-order Linear Odes
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(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)
= 1 and y'(b) = 2 and
be R.
(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.
Transcribed Image Text:(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) = 1 and y'(b) = 2 and be R. (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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