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Let y(t) be the continuously differentiable solution of the initial-value problem y" (t) +9y(t) = g(t), where y(0) = 1, y'(0) = 0, g(t) = {2 0 ≤ t≤ 4 - +9(t −4)² t > 4 (a) Find Y(s), the Laplace transform of y(t). (b) Compute y(t) for 0 < t < 4. (c) Compute y(t) for t > 4.

Let y(t) be the continuously differentiable solution of the initial-value problem y" (t) +9y(t) = g(t), where y(0) = 1, y'(0) = 0, g(t) = {2 0 ≤ t≤ 4 - +9(t −4)² t > 4 (a) Find Y(s), the Laplace transform of y(t). (b) Compute y(t) for 0 < t < 4. (c) Compute y(t) for t > 4.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 36CR
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Let y(t) be the continuously differentiable solution of the initial-value problem y" (t) +9y(t) = g(t), where y(0) = 1, y'(0) = 0, g(t) = {2 0 ≤ t≤ 4 - +9(t −4)² t > 4 (a) Find Y(s), the Laplace transform of y(t). (b) Compute y(t) for 0 < t < 4. (c) Compute y(t) for t > 4.
Transcribed Image Text:Let y(t) be the continuously differentiable solution of the initial-value problem y" (t) +9y(t) = g(t), where y(0) = 1, y'(0) = 0, g(t) = {2 0 ≤ t≤ 4 - +9(t −4)² t > 4 (a) Find Y(s), the Laplace transform of y(t). (b) Compute y(t) for 0 < t < 4. (c) Compute y(t) for t > 4.
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