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D) y y(0) c) y" + 4y + 3y = 8(t-2), y(0) = 1, y'(0) = -1

D) y y(0) c) y" + 4y + 3y = 8(t-2), y(0) = 1, y'(0) = -1

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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I only need help with part c

3. Solve the following initial value problems using the Laplace transform: a) \( y'' - 3y' + 2y = \delta(t - 1) \), \;\; \( y(0) = 1 \), \;\; \( y'(0) = 0 \) b) \( y'' - 4y = \delta(t - 3) \), \;\; \( y(0) = 0 \), \;\; \( y'(0) = 1 \) c) \( y'' + 4y' + 3y = \delta(t - 2) \), \;\; \( y(0) = 1 \), \;\; \( y'(0) = -1 \) d) \( y'' + 6y' + 13y = \delta(t - \frac{\pi}{4}) \), \;\; \( y(0) = 5 \), \;\; \( y'(0) = 5 \)
Transcribed Image Text:3. Solve the following initial value problems using the Laplace transform: a) \( y'' - 3y' + 2y = \delta(t - 1) \), \;\; \( y(0) = 1 \), \;\; \( y'(0) = 0 \) b) \( y'' - 4y = \delta(t - 3) \), \;\; \( y(0) = 0 \), \;\; \( y'(0) = 1 \) c) \( y'' + 4y' + 3y = \delta(t - 2) \), \;\; \( y(0) = 1 \), \;\; \( y'(0) = -1 \) d) \( y'' + 6y' + 13y = \delta(t - \frac{\pi}{4}) \), \;\; \( y(0) = 5 \), \;\; \( y'(0) = 5 \)
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