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b) Find the general solution for the following ODE 4y" +4y'+y=0 c) Find the particular solution of b) if y(0) = A and y'(0) = -A where A is a constant.

b) Find the general solution for the following ODE 4y" +4y'+y=0 c) Find the particular solution of b) if y(0) = A and y'(0) = -A where A is a constant.

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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5. 2nd order ODES a) For the following ODEs, find their eigenvalues and determine the type of damping (overdamped, undamped, underdamped, critically dam ped). For undamped and underdamped cases, find their angular frequency and period. i) y" +4y' +4y=0 ii) 4y"+16y' +17y=0 iii) y" +4y'=0 b) Find the general solution for the following ODE 4y" +4y'+y=0 c) Find the particular solution of b) if y(0) = A and y'(0) = -A where A is a constant.
Transcribed Image Text:5. 2nd order ODES a) For the following ODEs, find their eigenvalues and determine the type of damping (overdamped, undamped, underdamped, critically dam ped). For undamped and underdamped cases, find their angular frequency and period. i) y" +4y' +4y=0 ii) 4y"+16y' +17y=0 iii) y" +4y'=0 b) Find the general solution for the following ODE 4y" +4y'+y=0 c) Find the particular solution of b) if y(0) = A and y'(0) = -A where A is a constant.
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