Without solving explicitly, classify the critical points of the given first-order autonomous differential equation as either asymptotically stable or unstable. All constants are assumed to be positive. (Enter the critical points for each stability category as a comma-separated list. If there are no critical points in a certain category, enter NONE.) dx - k(a - x)(B - x)(y - x), a > B > y dt asymptotically stable unstable
Without solving explicitly, classify the critical points of the given first-order autonomous differential equation as either asymptotically stable or unstable. All constants are assumed to be positive. (Enter the critical points for each stability category as a comma-separated list. If there are no critical points in a certain category, enter NONE.) dx - k(a - x)(B - x)(y - x), a > B > y dt asymptotically stable unstable
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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Transcribed Image Text:Without solving explicitly, classify the critical points of the given first-order autonomous differential equation as either asymptotically stable or unstable. All constants are assumed to be positive. (Enter the critical
points for each stability category as a comma-separated list. If there are no critical points in a certain category, enter NONE.)
dx
— k(а — х)(в — х)(ү — х), а > В> Y
dt
asymptotically stable
X =
unstable
X =
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