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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) 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.

(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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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just b,c,d please!

(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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