a1 a12 Consider a differential equation of the form dx = Ax(t) where A = The eigenvalues of A are real, distinct, and nonzero. Analyze the stability of the equilibrium (0,0), and classify the equilibrium according to whether it a21 a22 is a sink, a source, or a saddle point. A = The eigenvalues v so the equilibrium is

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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dx
a11 a12
Consider a differential equation of the form
= Ax(t) where A =
dt
The eigenvalues of A are real, distinct, and nonzero. Analyze the stability of the equilibrium (0,0), and classify the equilibrium according to whether it
а21 а22
is a sink, a source, or a saddle point.
11
A =
0 2
.....
The eigenvalues
so the equilibrium is
Transcribed Image Text:dx a11 a12 Consider a differential equation of the form = Ax(t) where A = dt The eigenvalues of A are real, distinct, and nonzero. Analyze the stability of the equilibrium (0,0), and classify the equilibrium according to whether it а21 а22 is a sink, a source, or a saddle point. 11 A = 0 2 ..... The eigenvalues so the equilibrium is
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