ving nonlinear system of differential equations: x² - []=[x² 2²50] + y² - 50
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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Question
![**Consider the following nonlinear system of differential equations:**
\[
\begin{bmatrix}
x' \\
y'
\end{bmatrix}
=
\begin{bmatrix}
x^2 - y^2 \\
x^2 + y^2 - 50
\end{bmatrix}
\]
**The vector field and equilibria (critical points) are pictured below.**
[The image depicts a vector field with arrows indicating the direction of the field. There are several critical points marked on the graph, which show where the system's equilibria occur.]
**Compute the Jacobian matrix of this system (at a general point):**
[Blank space for computation]
**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.**
[Blank space for listing equilibria and classifying the type of each critical point.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd75c580-e1ed-40e9-aa84-8dd389134e22%2F56f75e44-fc1f-499d-8e3c-feed83fca99e%2Fpse9wcj_processed.png&w=3840&q=75)
Transcribed Image Text:**Consider the following nonlinear system of differential equations:**
\[
\begin{bmatrix}
x' \\
y'
\end{bmatrix}
=
\begin{bmatrix}
x^2 - y^2 \\
x^2 + y^2 - 50
\end{bmatrix}
\]
**The vector field and equilibria (critical points) are pictured below.**
[The image depicts a vector field with arrows indicating the direction of the field. There are several critical points marked on the graph, which show where the system's equilibria occur.]
**Compute the Jacobian matrix of this system (at a general point):**
[Blank space for computation]
**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.**
[Blank space for listing equilibria and classifying the type of each critical point.]
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