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21. Consider the equation ay" + by' + cy = 0, where a, b, and c are constants with a > 0. Find conditions on a, b, and c such that the roots of the characteristic equation are:

21. Consider the equation ay" + by' + cy = 0, where a, b, and c are constants with a > 0. Find conditions on a, b, and c such that the roots of the characteristic equation are:

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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21. Consider the equation ay" +by' + cy = 0, where a, b, and c are constants with a 0. Find conditions on a, b, and c such that the roots of the characteristic equation are: a. real, different, and negative. b. real with opposite signs. c. real, different, and positive. In each case, determine the behavior of the solution as t→→ 00.
Transcribed Image Text:21. Consider the equation ay" +by' + cy = 0, where a, b, and c are constants with a 0. Find conditions on a, b, and c such that the roots of the characteristic equation are: a. real, different, and negative. b. real with opposite signs. c. real, different, and positive. In each case, determine the behavior of the solution as t→→ 00.
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