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Eigenvalue Method

  1. Nov 1, 2009 #1
    1. The problem statement, all variables and given/known data
    solve the system dx/dt = [12 -6; 6 -3] with the initial value x(0) = [12; 9]


    2. Relevant equations



    3. The attempt at a solution
    I know I need to find the Eigenvalues but then I get a little confused from there.

    (λ-3)(λ+3)=0
    λ=3, -3
     
  2. jcsd
  3. Nov 2, 2009 #2

    HallsofIvy

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    Staff Emeritus
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    A assume you mean "dx/dt= [12 -6; 6 -3]x" or, in Latex,
    [tex]\frac{dX}{dt}= \frac{d\begin{bmatrix}x \\ y\end{bmatrix}}{dt}= \begin{bmatrix}12 & -6 \\ 6 & -3\end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}[/tex]


    That's wrong. Show us how you got the eigenvalue equation.
     
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