Answered: Analyze the stability of the critical…

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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Let g(x, y) = x³ – 6x² – y* + 5. Find and classify the critical point(s) of g.
Analyze the stability of the critical point of the following system, proposing as a Lyapunov function V(x,y)=ax2m+by2n. a) x′=−2xy, y′=x2−y3 b) x′=xy2−(x3/2), y′=−(y3/2)+(yx2/5) c) Show that x′=−2x+xy3, y′=−x2y2−y3 is asymptotically stable. Pleas be as clear as possible and legible. Show and explain all the steps in detail. Thank you very much.
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Analyze the stability of the critical point of the following system, proposing as a Lyapunov function V(x,y)=ax2m+by2n