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Decoupling ODE

  1. Apr 6, 2009 #1
    Hello, please can someone tell me how to decouple and solve this equation? It was on a problem sheet, but the solution jumped to the decoupled equation... =(

    [tex]
    \frac{dx}{dt} = 2x+y-t
    [/tex]
    [tex]
    \frac{dy}{dt}=2x-y+t
    [/tex]
    I know that it can rewritten as
    [tex]

    \frac{d}{dt}\left[ \begin{array}{cccc} 2 & 1\\ 2& -1 \end{array} \right] \left[\begin{array}{cccc} x\\ y \end{array}\right] + \left[ \begin{array}{cccc} -t\\ t \end{array} \right]

    [/tex]

    And for that matrix :

    [tex]

    \left[ \begin{array}{cccc} 2 & 1\\ 2& -1 \end{array} \right]

    [/tex]

    the eigenvalues and eigenvectors can be worked out.

    But I don't know how to decouple =(

    Thank you !
     
    Last edited: Apr 6, 2009
  2. jcsd
  3. Apr 6, 2009 #2

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Welcome to physics forums.

    HINT: Try differentiating one of the ODE's with respect to t.

    P.S. Since your question is a homework style question, I'm moving it to the homework forums.
     
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