Writing two first order equations in matrix form

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Homework Help Overview

The discussion revolves around writing two first order differential equations in matrix form, specifically the equations x' = y and y' = -x. The context includes a reference to a modified Van der Pol equation and a follow-up question regarding the fixed point of the system.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore how to express the given equations in matrix form and question the relevance of Jacobian matrices in this context. There is also a mention of using eigenvalue analysis to understand the system's behavior.

Discussion Status

The conversation includes attempts to clarify the matrix representation of the equations and the connection to eigenvalues. Some participants express uncertainty about the relationship between the original equations and Jacobian matrices, while others seek additional resources for understanding eigenvalue analysis.

Contextual Notes

Participants note the absence of a textbook and rely on a worksheet for exercises, which may limit their access to comprehensive explanations of the concepts involved.

andrey21
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I have been asked to write the following two first order equations in matrix form.


x' = y
y' = -x


I also must state that the follow on to the question asks for the only fixed point. The two first order equations came from a modified Van der pol equation.



 
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Jamiey1988 said:
I have been asked to write the following two first order equations in matrix form.


x' = y
y' = -x


I also must state that the follow on to the question asks for the only fixed point. The two first order equations came from a modified Van der pol equation.



Hint: Write the system of equations like this:
x' = 0x + 1y
y' = -1x + 0y
 
Ok would it be correct to write as a jacobian matrix?
If so would this be th answer?

0 1
-1 0
The numbers above are meant to be a matrix, sorry bad formatting:)
 
Jamiey1988 said:
Ok would it be correct to write as a jacobian matrix?
If so would this be th answer?

0 1
-1 0
The numbers above are meant to be a matrix, sorry bad formatting:)

Yes, that's the matrix, but I don't see how your problem is related to Jacobian matrices.
 
Well the next part of the question says:

Use eigen value analysis to describe the behaviour of the system.

Didnt want to put whole question on a single thread:)
 
Your book should have a section that describes the behavior of a system of differential equations based on the eigenvalues, whether they are real and positive, real and negative, complex, or pure imaginary.
 
Ah I don't actually have a book of such to use, just given a worksheet with exercises. COuld you direct me to a webpage with this information?
 

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