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9. Solve the IVPs. Sketch the solution. Describe the long term behavior. (a) y' + 3y = 2H(t− 3), y(0)=2 (b) y' + 3y = 28(t− 3), (c) y' + 3y = sin(at), y(0) = 2 y(0) = 0.

9. Solve the IVPs. Sketch the solution. Describe the long term behavior. (a) y' + 3y = 2H(t− 3), y(0)=2 (b) y' + 3y = 28(t− 3), (c) y' + 3y = sin(at), y(0) = 2 y(0) = 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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9. Solve the IVPs. Sketch the solution. Describe the long term behavior. (a) y' + 3y = 2(t-3), y(0) = 2 (b) y' + 3y = 28(t-3), y(0)=2 (c) y' + 3y = sin(at), (d) y" +9y=sin(t), y(0) = 0. y(0) = 0, y'(0) = 0
Transcribed Image Text:9. Solve the IVPs. Sketch the solution. Describe the long term behavior. (a) y' + 3y = 2(t-3), y(0) = 2 (b) y' + 3y = 28(t-3), y(0)=2 (c) y' + 3y = sin(at), (d) y" +9y=sin(t), y(0) = 0. y(0) = 0, y'(0) = 0
9. (a) y(t) = 2e-³t+ (1 − e9–³t) H (t − 3). y → 2/3 as t → ∞. (b) y(t) = 2e-3t+2e⁹-3t H(t− 3). y → 0 as t→∞. 1 cos(πt + p), p=tan ¹(3/π). (c) y(t) = ㅠ 9+7² -3t √9+ π² y(t) tends toward -√² cos(xt + 6). - (d) y(t) = (sin(3t) – sin(t))
Transcribed Image Text:9. (a) y(t) = 2e-³t+ (1 − e9–³t) H (t − 3). y → 2/3 as t → ∞. (b) y(t) = 2e-3t+2e⁹-3t H(t− 3). y → 0 as t→∞. 1 cos(πt + p), p=tan ¹(3/π). (c) y(t) = ㅠ 9+7² -3t √9+ π² y(t) tends toward -√² cos(xt + 6). - (d) y(t) = (sin(3t) – sin(t))
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