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Fundamental set of solutions

  1. Mar 19, 2008 #1
    1. The problem statement, all variables and given/known data
    Find a fundamental set of solutions to the system of differential equations:

    y1' = 3*y1 - y2

    y2' = y1 + y2

    by reducing the problem to Jordan Canonical Form.

    2. Relevant equations

    y' = Ay
    J = P[tex]^{-1}[/tex]AP

    3. The attempt at a solution
    I have found the following:

    (1) y' = Ay implies
    A =
    3 -1
    1 1

    (2) lamda (eigenvalue) = 2 with multiplicity 2

    (3) So I believe
    J (JCF) =
    2 1
    0 2

    and P =
    1 1
    1 0

    so that J = P[tex]^{-1}[/tex]AP

    Now I'm stuck. How do I use this to produce the fundamental set of solutions? Any help appreciated.
  2. jcsd
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