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Diff Eq problem

  1. Apr 28, 2008 #1
    [SOLVED] Diff Eq problem

    1. The problem statement, all variables and given/known data
    y'' - 3y' - 4y= 5e^-x - 3x^2 + 7

    2. Relevant equations

    I think I would need to find complimentary solution, then the particular solution using variation of parameters
    y=y(c) + y(p)

    3. The attempt at a solution

    (r-4)(r+1)=0, r=4,-1

    this is where I get stuck as I do not know what to use for y(p), would it be
    y(p)=Axe^-x + Bx^2 + Dx +E ???
    y'(p)=Ae^-x - Axe^-x + 2Bx + D
    y"(p)=-Ae^-x -Ae^-x +Axe^-x +2B= Axe^-x - 2Ae^-x + 2B

    (Axe^-x - 2Ae^-x + 2B) - 3(-Axe^-x + Ae^-x + 2Bx + D) -4(Axe^-x +Bx^2 + Dx +E)= (5e^-x - 3x^2 + 7)

    am I even heading in the right direction?
    Last edited: Apr 28, 2008
  2. jcsd
  3. Apr 28, 2008 #2
    everything looks right so far. now you just want to collect terms and match coefficients.
  4. Apr 28, 2008 #3


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    Homework Helper

    If I remember correctly that is not variation of parameters but method of undermined coefficients. Variation of parameters is something different.
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