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How to use matrices to solve systems of ODEs?

  1. Sep 25, 2004 #1
    I'm dealing with systems of 3 differential equations that are all coupled to each other. Fortunately, all the ODEs are first order.

    Can somebody give me a primer of how to use matrices to solve these problems?

    here's an example:

    Say we have a system of 3 ODEs all coupled to each other:

    Mx, My, Mz

    dMx/dt = A*Mx + B*My + C*Mz

    dMy/dt = D*Mx + E*My + F*Mz

    dMz/dt = G*Mx + H*My + J*Mz

    So the matrix would be:

    dM/dt = [A B C
    D E F
    G H J] M + [K L M]

    So what do I do now? Diagonalize the matrix and then find eigenvectors? Whats the step by step?
  2. jcsd
  3. Sep 26, 2004 #2


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    That's right.
    Now, suppose you've got a diagonal matrix.
    What are the functions satisfying those differential equations?
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