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Homework Help: Complex Eigenvalues

  1. Mar 20, 2012 #1
    1. The problem statement, all variables and given/known data
    Apply the eigenvalue method to find a general solution of the given system.
    [tex]x_1' = 5x_1 - 9x_2[/tex]
    [tex]x_2' = 2x_1 - x_2[/tex]

    2. Relevant equations

    3. The attempt at a solution
    [tex]x_1' = 5x_1 - 9x_2[/tex]
    [tex]x_2' = 2x_1 - x_2[/tex]

    5-λ & -9\\
    2 & -1-λ
    [tex](λ-2)^2 -9=0[/tex]
    So I plugged λ into the matrix;
    3-3i & -9\\
    2 & -3-3i
    This is where I'm stuck...the answer is;
    [tex]x_1(t)=3e^{2t}(c_1cos2t - 5c_2sin2t)[/tex]
    [tex]x_2(t)=e^{2t}[(c_1+c_2)cos3t + (c_1-c_2)sin3t)][/tex]
  2. jcsd
  3. Mar 21, 2012 #2
    Any one?
  4. Mar 21, 2012 #3


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    Science Advisor

    This is your error. [itex](\lambda- 2)^2- 9= 0[/itex] is equivalent to [itex](\lambda- 2)^2= 9[/itex] so [itex]\lambda- 2= \pm 3[/itex]. There is no "i".

    There are no eigenvectors because 2+ 3i and 2- 3i are not eigenvalues.
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