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Take the conservative equation " + x² - 9 = 0. Write down the corresponding first order system using the extra variable y: x' = y' = The critical points are on the x-axis at the following two x values (order them as they are on the number line): Compute the Jacobian matrix for all x and y: The behavior at the first critical point is The behavior at the second critical point is For behavior write one of: "saddle", "source", "sink", "spiral sink", "spiral source", "center".

Take the conservative equation " + x² - 9 = 0. Write down the corresponding first order system using the extra variable y: x' = y' = The critical points are on the x-axis at the following two x values (order them as they are on the number line): Compute the Jacobian matrix for all x and y: The behavior at the first critical point is The behavior at the second critical point is For behavior write one of: "saddle", "source", "sink", "spiral sink", "spiral source", "center".

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 16EQ
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Take the conservative equation " + x² - 9 = 0. Write down the corresponding first order system using the extra variable y: x' = y' The critical points are on the x-axis at the following two x values (order them as they are on the number line): Compute the Jacobian matrix for all x and y: The behavior at the first critical point is The behavior at the second critical point is For behavior write one of: "saddle", "source", "sink", "spiral sink", "spiral source", "center".
Transcribed Image Text:Take the conservative equation " + x² - 9 = 0. Write down the corresponding first order system using the extra variable y: x' = y' The critical points are on the x-axis at the following two x values (order them as they are on the number line): Compute the Jacobian matrix for all x and y: The behavior at the first critical point is The behavior at the second critical point is For behavior write one of: "saddle", "source", "sink", "spiral sink", "spiral source", "center".
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