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Second-Order Equations and Eigenvectors

  1. Nov 30, 2011 #1
    1. The problem statement, all variables and given/known data

    Convert y"=0 to a first-order system du/dt=Au

    d/dt [y y']T = [y' 0]T = [0 1; 0 0] [y y']T

    This 2x2 matrix A has only one eigenvector and cannot be diagonalized. Compute eAt from the series I+At+... and write the solution eAtu(0) starting from y(0)=3, y'(0)=4. Check that your (y, y') satisfies y"=0.

    2. Relevant equations



    3. The attempt at a solution

    So I found eAt to be equal to the matrix
    [1 t
    0 1].
    I found this eAt=I+At where A is the matrix [0 1; 0 0].

    I also know that matrix A has eigenvalue 0 with multiplicity 2, and eigenvector [1 0]T.

    But from there I'm stuck... Not sure how to get eAtu(0)...

    Can anyone help? Thanks in advance!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 30, 2011 #2

    I like Serena

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    Hi again!

    How is u defined in your problem?

    And do you have a relevant equation for solving a linear system of first order differential equations?
     
  4. Nov 30, 2011 #3
    That's why I'm so confused... The only information given is the one I stated above exactly as it is worded. And I don't know of any relevant equations for solving this system. :-(
     
  5. Nov 30, 2011 #4

    I like Serena

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    In your problem statement you write du/dt.
    And then you write d/dt [y y']^T.

    Are they related?
     
  6. Nov 30, 2011 #5
    Nevermind. I think I figured it out. Thanks for the help!!!
     
  7. Nov 30, 2011 #6

    I like Serena

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    Ok.
    (Did you find your relevant equation?)
     
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