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Variation of Parameters

  1. Oct 18, 2009 #1
    1. The problem statement, all variables and given/known data
    Find a particular solution to:

    y''+4y=20sec(2t)


    2. Relevant equations



    3. The attempt at a solution
    y''+4y=0
    r^2+4=0
    r=+or- 2i

    So, yc(t) = Asin(2t) + Bcos(2t)
    yp(t)= -cos(2t) ∫ 10sin(2t)sec(2t)dt + sin(2t) ∫ 10cos(2t)sec(2t)dt
    = -10cos(2t) ∫ tan(2t)dt+10sin(2t) ∫ 1dt
    = -10cos(2t)(-.5ln(cos(2t)))+10tsin(2t)

    I don't know what's wrong. Can anyone help me out?
     
  2. jcsd
  3. Oct 19, 2009 #2

    rock.freak667

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    Homework Helper

    I don't know if you did it in your integrands but did you happen to divide R(x)y1(x) by W(y1,y2) where W is the wronskian ?
     
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