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Homework Help: Differential Equations: Variation of Parameters

  1. Apr 18, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the particular solution to the differential equation using method of variation of parameters:

    4y''-4y'+y=16e^(t/2)


    3. The attempt at a solution

    Set 4y''-4y'+y=0

    then the homogeneous solution is:

    y= c1*e^(t/2)+c2*te(t/2)

    set y1= e^(t/2), y2= te^(t/2)

    then y1' = (1/2)*e^(t/2), y2' = (t/2+1)*e^(t/2)

    Wronskian = W(y1,y2) = e^t

    http://img140.imageshack.us/img140/1822/dif1.jpg [Broken]


    I know i did something wrong because checking my answer by plugging Y(t) back in to the O.D.E , left hand side and right hand side dont check out.

    By using method of undetermined coefficients, Y(t) = 2t^2*e^(t/2), which is the correct answer.

    So question is what did i do wrong using method of variation of parameters?

    Thanks
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 20, 2010 #2
    nevermind, i figured it out myself
     
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