5. Laplace Transforms (a) Use the theorem of derivatives of Laplace transforms to: i. 2ks (s²-k²)2. (b) Use the Laplace Transform to solve the following ODES: i. x" + 4x cost, x(0) = 0 = x'(0); x" - 4x = 3t, x(0) = 0 = x¹(0). ii. compute L[cosh kt] directly from the formula for L[sinh kt]; show that C[t sinhkt ii. = =
5. Laplace Transforms (a) Use the theorem of derivatives of Laplace transforms to: i. 2ks (s²-k²)2. (b) Use the Laplace Transform to solve the following ODES: i. x" + 4x cost, x(0) = 0 = x'(0); x" - 4x = 3t, x(0) = 0 = x¹(0). ii. compute L[cosh kt] directly from the formula for L[sinh kt]; show that C[t sinhkt ii. = =
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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![5. Laplace Transforms
(a) Use the theorem of derivatives of Laplace transforms to:
i.
ii.
2ks
(s²-k²)2.
(b) Use the Laplace Transform to solve the following ODES:
i.
x" + 4x = cost, x(0) = 0 = x²(0);
x" - 4x = 3t, x(0) = 0 = x¹(0).
compute L[cosh kt] directly from the formula for L[sinh kt];
show that C[t sinhkt
ii.
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba18de34-fc06-47a6-b1ea-c54726b84874%2F5d412d35-e646-4698-924f-08457c497924%2Fua1td4g_processed.png&w=3840&q=75)
Transcribed Image Text:5. Laplace Transforms
(a) Use the theorem of derivatives of Laplace transforms to:
i.
ii.
2ks
(s²-k²)2.
(b) Use the Laplace Transform to solve the following ODES:
i.
x" + 4x = cost, x(0) = 0 = x²(0);
x" - 4x = 3t, x(0) = 0 = x¹(0).
compute L[cosh kt] directly from the formula for L[sinh kt];
show that C[t sinhkt
ii.
=
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