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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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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