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Homework Help: Little confused

  1. Oct 11, 2005 #1
    hi all i have a bit of a problem here, it has to do with completing the cube.

    here is the problem

    y''' +y' + 2y = 0

    i am trying to sove by the methoed of constant coefficients
     
  2. jcsd
  3. Oct 11, 2005 #2

    HallsofIvy

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    So your characteristic equation is r3+ r+ 2= 0.

    One of the things I notice immediately is that (-1)3+ (-1)+ 2= 0. Does that help?
     
  4. Oct 11, 2005 #3

    saltydog

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    So how do you divide r+1 into [itex]r^3+r+2[/itex]?

    Well r goes into [itex]r^3, r^2[/itex] times right? So that means:

    [tex]r^2(r+1)=r^3+r^2[/tex]

    and:

    [tex](r^3+r+2)-(r^3+r^2)=-r^2+r+2[/tex]

    Ok, we got the first one: [itex]r^2[/itex]

    Now, how do you divide r+1 into [itex]-r^2+r+2[/itex]

    Keep doin' that to get to the quadratic form of the remaining roots, remainder at end is 0 if -1 is a root. You know how to do this right?
     
    Last edited: Oct 11, 2005
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