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".
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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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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