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
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Chapter2: Second-order Linear Odes
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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 =
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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