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3rd order ODE

  1. Jul 17, 2011 #1
    I am stuck on solving for the roots of a charactristic equation:

    y'''- y''+y'-y=0

    where I set r^3-r^2+r-1=0 and factored out r to get r*[ r^2-r +1] -1 =0 to get the real root of 1. How can I solve for the compex roots?
     
  2. jcsd
  3. Jul 17, 2011 #2

    SteamKing

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    By inspection, r = 1 is a root of your characteristic equation.
    In order to find the other roots, you should factor (r - 1) from the char. eq.
     
  4. Jul 17, 2011 #3

    hunt_mat

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    So what I would do is write:
    [tex]
    (r-1)(ar^{2}+br+c)=r^{3}-r^{2}+r-1
    [/tex]
    Expand and equate coefficients, then solve the quadratic
     
  5. Jul 17, 2011 #4
    Typically people use long division. But in this case it's obvious that the other factor is r^2+1.

    Or you could just go to Wolfram Alpha and say "factor r^3-r^2+r-1" :-)
     
    Last edited: Jul 17, 2011
  6. Jul 17, 2011 #5

    hunt_mat

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    I never really understood long division.
     
  7. Jul 18, 2011 #6
    Got it now, thanks
     
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