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6. Solve the following differentiation equations with the method of unde- termined coefficients to find the particular solution. (i) y" - 2y + 2y = cos(t); y(0) = 1, y'(0) = 0 (ii) y" + 2y' + y = 4et; y(0) = 2, y'(0) = -1

6. Solve the following differentiation equations with the method of unde- termined coefficients to find the particular solution. (i) y" - 2y + 2y = cos(t); y(0) = 1, y'(0) = 0 (ii) y" + 2y' + y = 4et; y(0) = 2, 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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Hi, I need help with all parts. I have attached the solutions. 6. Solve the following differentiation equations with the method of unde- termined coefficients to find the particular solution. (i) y" - 2y + 2y = cos(t); y(0) = 1, y'(0) = 0 (ii) y" + 2y + y = 4e t; y(0) = 2, y'(0) = -1 6. (i) y = (cos(t) - 2 sin(t) + 4e* cos(t) — 2et sin(t)) (ii) y = 2e-t+te-t +2t²e-t
Transcribed Image Text:Hi, I need help with all parts. I have attached the solutions. 6. Solve the following differentiation equations with the method of unde- termined coefficients to find the particular solution. (i) y" - 2y + 2y = cos(t); y(0) = 1, y'(0) = 0 (ii) y" + 2y + y = 4e t; y(0) = 2, y'(0) = -1 6. (i) y = (cos(t) - 2 sin(t) + 4e* cos(t) — 2et sin(t)) (ii) y = 2e-t+te-t +2t²e-t
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