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Systems of difeq

  1. Apr 11, 2009 #1
    1. The problem statement, all variables and given/known data
    http://img412.imageshack.us/img412/6463/difeq.jpg [Broken]


    2. Relevant equations

    Matrix maniupation, egein values, determinant, etc

    3. The attempt at a solution

    Well, at first I tried the formulaic way, i.e. finding the eigenvalue through the determinant, but it gave me zero and worse when plugged in it gives zero for x1 and x2.

    It seems it is too simple to use matrixes here so Instead I just tried it the old fashioned way - i.e. solving for the system through calculus and algebra.

    So

    x1'=-20x1
    x2'=-10x1

    So I solved for x1 because it seemed pretty straightforward and it was, I got:

    x1=8exp(-20t)

    which is correct

    So now I try plugging it in x2' and integrating dx2/dt and I get

    x2-8=2exp(-20t)/5-2/5

    which should give

    x2=2exp(-20t)/5-2/5+8

    However this is wrong. can someone help me with this?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 11, 2009 #2

    Pengwuino

    User Avatar
    Gold Member

    When you plugged in x1, you forgot to multiply by -10 and your integration came out incorrectly.

    Also, an eigenvalue of 0 is perfectly acceptable. It's simply a constant solution.
     
    Last edited: Apr 11, 2009
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