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Laplace Transform of Systems of ODEs with variable coefficients

  1. Dec 13, 2011 #1
    1. The problem statement, all variables and given/known data
    Say you have:

    EQ1: y1''*t+y1'*t+y2=0

    and

    EQ2: y2''*t+y2'*t+y1=0

    y1(0)=0,y1'(0)=0,y2(0)=0,y2'(0)=0


    2. Relevant equations



    3. The attempt at a solution

    I can get it so far, but having both y1 and y2 really gives me fits:

    Eq1: Y1(-2s-1)+dY1/ds(-s2-s)=-Y2

    Eq2: Y2(-2s-1)+dY2/ds(-s2-s)=-Y1

    I try to shift it around to be dY1/Y1 = (-2s-1)/(-s2-s)-Y2/Y1(-s2-s)

    But then I just don't know to do the integrations given you have both Ys. I just can't separate them.

    Any help would be appreciated.
     
  2. jcsd
  3. Dec 14, 2011 #2

    I like Serena

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    Homework Helper

    Welcome to PF, physics19921! :smile:

    You can't separate the Ys?
    So don't.
    Add them, and subtract them respectively.

    That is, add the 2 equations and solve for z1=(y1+y2).
    Then subtract the 2 equations and solve for z2=(y1-y2).
    Finally combine the solutions...
     
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