In each of Problems 17 and 18, determine the values of a, if any, for which all solutions tend to zero as t→∞o; also determine the values of a, if any, for which all (nonzero) solutions become unbounded as t→∞. 17. y" - (2x - 1)y' + a(a - 1)y=0 18. y" +(3-a) y' -2(a - 1) y = 0
In each of Problems 17 and 18, determine the values of a, if any, for which all solutions tend to zero as t→∞o; also determine the values of a, if any, for which all (nonzero) solutions become unbounded as t→∞. 17. y" - (2x - 1)y' + a(a - 1)y=0 18. y" +(3-a) y' -2(a - 1) y = 0
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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![In each of Problems 17 and 18, determine the values of \(\alpha\), if any, for which all solutions tend to zero as \(t \to \infty\); also determine the values of \(\alpha\), if any, for which all (nonzero) solutions become unbounded as \(t \to \infty\).
**17.** \[ y'' - (2\alpha - 1)y' + \alpha(\alpha - 1)y = 0 \]
**18.** \[ y'' + (3 - \alpha)y' - 2(\alpha - 1)y = 0 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffddfa066-ae14-4710-b68e-f1412b1153a3%2F58d0a3c0-90cb-4b88-9726-187791e82488%2Fh4dtlxy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In each of Problems 17 and 18, determine the values of \(\alpha\), if any, for which all solutions tend to zero as \(t \to \infty\); also determine the values of \(\alpha\), if any, for which all (nonzero) solutions become unbounded as \(t \to \infty\).
**17.** \[ y'' - (2\alpha - 1)y' + \alpha(\alpha - 1)y = 0 \]
**18.** \[ y'' + (3 - \alpha)y' - 2(\alpha - 1)y = 0 \]
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