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Diff Eq: Initial Value Prob

  1. Feb 8, 2005 #1
    I'm hacking at this particular linear system:

    dY/dt = [1, -1; 1, 3] Y

    I've already found myself a solution using the following function:

    Y(t) = [ te^(2t), -(t+1)e^(2t) ]

    That was fun, actually, once I figured out what the hell I was doing.

    Here's my question: the next part of the problem asks for a solution to the intial value problem of the above differential equation, where

    Y(0) = [0, 2]

    I'm not sure how to attack the problem. Do I sub that matrix in for both values of Y, on both sides? If I do, then where do I put Y(t) so that this works out correctly? Or is there some other matrix multiplication step that I'm missing?

    Any ideas?

    Thanks in advance.

  2. jcsd
  3. Feb 9, 2005 #2


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    Science Advisor
    Homework Helper

    You have a solution for the system. Generally, you will have a superpostion of two linearly independent solutions and you will adjust their coefficients to match the initial values.
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