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(a) Find the fundamental set of solutions of the following equations (a1) 2y" +2y' — 40y = 0 - - (a2) y" + 2y' — 5y = 0 (a3) y" + 8y' + 16y = 0 (b) For each of these general (fundamental) solutions, find c₁ and c₂ such that y(0) and y'(0) = 1. = 1 (c) For each of these general (fundamental) solutions, discuss how c₁ and c₂ affect the long term behavior of the solutions

(a) Find the fundamental set of solutions of the following equations (a1) 2y" +2y' — 40y = 0 - - (a2) y" + 2y' — 5y = 0 (a3) y" + 8y' + 16y = 0 (b) For each of these general (fundamental) solutions, find c₁ and c₂ such that y(0) and y'(0) = 1. = 1 (c) For each of these general (fundamental) solutions, discuss how c₁ and c₂ affect the long term behavior of the solutions

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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(a) Find the fundamental set of solutions of the following equations (a1) 2y" +2y' — 40y = 0 - - (a2) y" + 2y' — 5y = 0 (a3) y" + 8y' + 16y = 0 (b) For each of these general (fundamental) solutions, find c₁ and c₂ such that y(0) and y'(0) = 1. = 1 (c) For each of these general (fundamental) solutions, discuss how c₁ and c₂ affect the long term behavior of the solutions
Transcribed Image Text:(a) Find the fundamental set of solutions of the following equations (a1) 2y" +2y' — 40y = 0 - - (a2) y" + 2y' — 5y = 0 (a3) y" + 8y' + 16y = 0 (b) For each of these general (fundamental) solutions, find c₁ and c₂ such that y(0) and y'(0) = 1. = 1 (c) For each of these general (fundamental) solutions, discuss how c₁ and c₂ affect the long term behavior of the solutions
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