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Eigenvalues for Equilibrium Points of First Order Nonlinear DE

  1. Feb 11, 2012 #1

    jsi

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    1. The problem statement, all variables and given/known data

    dy/dx = y^3-3y^2+2y
    it's asking for equilibrium points and for the eigenvalues and stability at each point.

    2. Relevant equations



    3. The attempt at a solution

    I found the equilibrium points by setting dy/dx = 0 as we were taught to do in class and got y = 0, 1, 2. Then I took the derivative of the equation and evaluated it at each point to determine stability and found derivative at 0 = 2, at 1 = -1, and at 2 = 2 so the first and third are unstable and the second is stable. I'm confused on how to find eigenvalues for just one equation because I'm used to doing it for 2 equations. Have I already done it by evaluating the equilibrium points at the derivative and those are the eigenvalues or is there more to it? Thanks!
     
  2. jcsd
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