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Find the general solution to the following: (a) 6y"+y'- y = 0. (b) y" + 8y' + 16y = 0. (c) y" + 2y' + 3y = 0. Then, for (a)-(c) describe the possible behaviors of the solution, e.g., "for constants C₁, C2 > 0 the function tends to ∞o as too."

Find the general solution to the following: (a) 6y"+y'- y = 0. (b) y" + 8y' + 16y = 0. (c) y" + 2y' + 3y = 0. Then, for (a)-(c) describe the possible behaviors of the solution, e.g., "for constants C₁, C2 > 0 the function tends to ∞o as too."

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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Find the general solution to the following: (a) 6y"+y' - y = 0. (b) y" + 8y' + 16y = 0. (c) y" + 2y' + 3y = 0. Then, for (a)-(c) describe the possible behaviors of the solution, e.g., "for constants C₁, C2 > 0 the function tends to ∞ as t→∞."
Transcribed Image Text:Find the general solution to the following: (a) 6y"+y' - y = 0. (b) y" + 8y' + 16y = 0. (c) y" + 2y' + 3y = 0. Then, for (a)-(c) describe the possible behaviors of the solution, e.g., "for constants C₁, C2 > 0 the function tends to ∞ as t→∞."
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