2. (Laplace Transforms) (a) Use the definition of the Laplace transform to compute L{cos(a + t)}, where a € R. What's the domain of L{cos(a + t)}? (b) Use Laplace transforms to solve y" - a²y = cos(a + t) where y(0) = 1 and y' (0) = 2. (c) Is the solution in part (b) unique? Justify using a theorem.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. (Laplace Transforms)
(a) Use the definition of the Laplace transform to compute L{cos(a + t)}, where a € R.
What's the domain of L{cos(a +t)}?
(b) Use Laplace transforms to solve y" - a²y:
=
= cos(a + t) where y(0) = 1 and y'(0) = 2.
(c) Is the solution in part (b) unique? Justify using a theorem.
1
(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:2. (Laplace Transforms) (a) Use the definition of the Laplace transform to compute L{cos(a + t)}, where a € R. What's the domain of L{cos(a +t)}? (b) Use Laplace transforms to solve y" - a²y: = = cos(a + t) where y(0) = 1 and y'(0) = 2. (c) Is the solution in part (b) unique? Justify using a theorem. 1 (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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