Consider the pair of differential equations dr =1- V. dt dy = r² – y°. dt (a) Find all the equilibrium points of these equations. (b) Classify each equilibrium point of this non-linear system as far as possible by considering the Jacobian matrix.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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Consider the pair of differential equations
dr
=1- V.
dt
dy
= r² – y°.
dt
(a) Find all the equilibrium points of these equations.
(b) Classify each equilibrium point of this non-linear system as far as
possible by considering the Jacobian matrix.
Transcribed Image Text:Consider the pair of differential equations dr =1- V. dt dy = r² – y°. dt (a) Find all the equilibrium points of these equations. (b) Classify each equilibrium point of this non-linear system as far as possible by considering the Jacobian matrix.
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