For each of the following systems, find appropriate values of m, n,a, such thatV(x, y) = x+ay" is a Liapunov function and hence show that the equilibrium pointat the origin is asymptotically stable.x = y − x(x² + y²)ddtddty = − x − x²y.

To find the appropriate values of m, n, and a for the given system, we need to ensure that the…

Answered: For each of the following systems, find…

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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For each of the following systems, find appropriate values of m, n,a, such that V(x, y) = x+ay" is a Liapunov function and hence show that the equilibrium point at the origin is asymptotically stable. x = y − x(x² + y²) d dt d dt y = − x − x²y.