Suppose there exists an equilibrium point x* E R" of a system of first order differ- ential equations such that every solution x(t) of the system satisfies limt∞ x(t) = x*, then the equilibrium point x* is asymptotically stable.

Suppose there exists an equilibrium point x* E R" of a system of first order differ- ential equations such that every solution x(t) of the system satisfies limt∞ x(t) = x, then the equilibrium point x is asymptotically stable.

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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Question

State True or False in each of the following cases. In one or two sentences justifiy each of your answers providing examples if relevant.

Suppose there exists an equilibrium point x* E R" of a system of first order differ-
ential equations such that every solution x(t) of the system satisfies limt→ x(t) = x*, then the
equilibrium point x* is asymptotically stable.

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