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Finding General Solution / Fundamental matrix

  1. Dec 8, 2009 #1
    Morning everyone,

    Studying for a test and having a problem on a practice question he gave us to study with. Here's the question along with the answer:

    Y' = AY + [e^t
    e^-t
    0]

    with A =
    [-1 0 4
    -0 -1 2
    0 0 1]

    the answer given is: Y(t) =
    [1/2(e^t - e^-t)
    e^-t(t+1)
    0]

    My question is, what are the steps to getting to this solution, I've gone over notes, examples, scavenged the internet, not a whole lot of luck. I know it's probably out there, but I am probably looking up the wrong keywords via Google.

    Any help with a general outline of what to do would be extremely helpful! Thanks a lot!

    p.s. sorry for bad formatting
     
  2. jcsd
  3. Dec 8, 2009 #2
    You can search for the matrix exponential, and state equation in any linear systems book.

    [tex]
    \dot x = Ax+Bu
    [/tex]

    is the form that you are looking for. The solution is a not-so-complicated convolution integral
     
  4. Dec 8, 2009 #3
    ok so what I am looking for is the state equation and matrix exponential?

    this type of problem ended up not being on the exam,but I am guessing it will show up on the final in a just over a week.
     
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