Writing two first order equations in matrix form

[andrey21]

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.

 

[Mark44]

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

 

[andrey21]

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:)

 

[Mark44]

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.

 

[andrey21]

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:)

 

[Mark44]

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.

 

[andrey21]

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?