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a. b. C. Find the function g(t) whose Laplace transform is given by T (7²+4)² Hint: Find F such that -F' = G, and use L[sf(s)] = − F'(T) graph: G(T) = Find the Laplace transform of the function h: [0, ∞) → R with the following Solve the initial value problem using the Laplace transform method y"+y = 2h(t), y(0) = y'(0) = 0, where h is the function given in (b). t> 0,

a. b. C. Find the function g(t) whose Laplace transform is given by T (7²+4)² Hint: Find F such that -F' = G, and use L[sf(s)] = − F'(T) graph: G(T) = Find the Laplace transform of the function h: [0, ∞) → R with the following Solve the initial value problem using the Laplace transform method y"+y = 2h(t), y(0) = y'(0) = 0, where h is the function given in (b). t> 0,

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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question b c d，ODE 

d. determine: h(t) 4π 3π 2π ㅠ ㅠ 2π 3π 4π 5π 6TT 7π (i) if y remains bounded as t → ∞; (ii) if y converges as t→∞ (if so, what is the limit). 8π t Analyze the behavior of the solution y from (c) as t → ∞. Particularly,
Transcribed Image Text:d. determine: h(t) 4π 3π 2π ㅠ ㅠ 2π 3π 4π 5π 6TT 7π (i) if y remains bounded as t → ∞; (ii) if y converges as t→∞ (if so, what is the limit). 8π t Analyze the behavior of the solution y from (c) as t → ∞. Particularly,
a. b. C. Find the function g(t) whose Laplace transform is given by graph: G(T) = Hint: Find F such that -F' = G, and use L[sf(s)] = − F'(T) - T (7²+4)² Find the Laplace transform of the function h: [0, ∞)→ R with the following Solve the initial value problem using the Laplace transform method where h is the function given in (b). y" + y = 2h(t), y(0) = y′(0) = 0, t> 0,
Transcribed Image Text:a. b. C. Find the function g(t) whose Laplace transform is given by graph: G(T) = Hint: Find F such that -F' = G, and use L[sf(s)] = − F'(T) - T (7²+4)² Find the Laplace transform of the function h: [0, ∞)→ R with the following Solve the initial value problem using the Laplace transform method where h is the function given in (b). y" + y = 2h(t), y(0) = y′(0) = 0, t> 0,
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