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Writing two first order equations in matrix form

  1. Apr 12, 2010 #1
    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.



     
  2. jcsd
  3. Apr 12, 2010 #2

    Mark44

    Staff: Mentor

    Hint: Write the system of equations like this:
    x' = 0x + 1y
    y' = -1x + 0y
     
  4. Apr 12, 2010 #3
    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:)
     
  5. Apr 12, 2010 #4

    Mark44

    Staff: Mentor

    Yes, that's the matrix, but I don't see how your problem is related to Jacobian matrices.
     
  6. Apr 12, 2010 #5
    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:)
     
  7. Apr 12, 2010 #6

    Mark44

    Staff: Mentor

    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.
     
  8. Apr 12, 2010 #7
    Ah I dont 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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