(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.
(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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![(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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ae14ade-6f74-4154-97ef-b44e7d0350a4%2F185ce30d-910f-45f6-8fe3-71d5936f76c0%2F6w20st_processed.png&w=3840&q=75)
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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