Let y(t) be the continuously differentiable solution of the initial-value problemy" (t) +9y(t) = g(t),wherey(0) = 1, y'(0) = 0,g(t)={20 ≤ 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.

Step 1: Step 2: Step 3: Step 4:

Answered: Let y(t) be the continuously…

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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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.