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Systems of ODE's double-zero eigenvalues

  1. May 8, 2010 #1
    1. The problem statement, all variables and given/known data
    Image.jpg I put a triangle around the problem of interest.


    2. Relevant equations



    3. The attempt at a solution
    I solved for the eigenvalues, resulting in double-zero values. My question is, using the variation of parameters method, which is what (14) refers to in the question. How do I solve for the second zero. For the first I get the matrix

    ([1]) *c1 for the general solution.
    ([1])

    Do I need to add a guess such as t to the next zero eigenvalue?
     
  2. jcsd
  3. May 8, 2010 #2

    lanedance

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    Homework Helper

    yeah so as you say, a constant value is your 1st general solution, i would try multplying by t and whether you can find a 2nd...

    note also, that the column vectors of the matrix are the linearly dependent, and that x1' = x2' for all t
     
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