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Math Help - Challenging Dif EQ

  1. #1
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    Challenging Dif EQ

    Given the following Dif EQ's (linear):

    \textbf{X}'=\left(\begin{array}{rr}-1 & c \\ 1 & -1 \end{array}\right)\textbf{X}

    Determine the values of c, where c is a constant, for which every solution \textbf{X} has the property where \textbf{X}(t)\rightarrow \textbf{0} as t\rightarrow \infty
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  2. #2
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    Is there a determinant property that will solve this?
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    Is there a determinant property that will solve this?
    I was thinking that maybe I have to do the Wronskian on this, but I'm not entirely sure.
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  4. #4
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    I plugged this in Maple, and found the eigenvalues and corresponding eigenvectors in terms of c.

    The two eigenvalues are:

    -1+\sqrt{c}

    -1-\sqrt{c}

    The corresponding eigenvectors, respectively, are:

    [sqrt(c),1]

    [-sqrt(c),1]

    The multiplicities of both are 1. Not sure where to go with this...

    When c = 0, we have repeated eigenvalues ...

    When c is negative, we have complex numbers... I can't imagine complex numbers yielding X(t) -> 0 with t -> infinity ....

    Ahh, very challenging.
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