ving nonlinear system of differential equations: x² - []=[x² 2²50] + y² - 50

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 32E
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Consider the following nonlinear system of differential equations:
[]=[²50]
x² + y² - 50
The vector field and equilibria (critical points) are pictured below.
Compute the jacobian matrix of this system (at a general point):
Find all the equilibria of the system, and for each of them in the order you would read them if they were words on a page (i.e. top-to-
bottom, left-to-right) - give the information requested below. The type of the critical point is "saddle", "nodal source", etc.
Transcribed Image Text:Consider the following nonlinear system of differential equations: []=[²50] x² + y² - 50 The vector field and equilibria (critical points) are pictured below. Compute the jacobian matrix of this system (at a general point): Find all the equilibria of the system, and for each of them in the order you would read them if they were words on a page (i.e. top-to- bottom, left-to-right) - give the information requested below. The type of the critical point is "saddle", "nodal source", etc.
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