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Working backwords from solution to DE

  1. Feb 28, 2015 #1
    1. The problem statement, all variables and given/known data
    if y = c1*e^t*sin(√3t)+c2*e^t*cos(√3t) + sintcost


    3. The attempt at a solution

    I have already figured out that (2±√-12)/2 so b = -2 and -12 = 4-4c so c = 4 and a = 1
    and that means that the associated homogeneous DE is y'' -2y' + 4y = 0, but I don't know what to do about the sintcost to get then g(t) in y'' -2y' + 4y = g(t), I have tried looking at different methods of solving 2nd order differential equations and tried working backwards but I can't get anything going. What would a good first step be?
     
  2. jcsd
  3. Feb 28, 2015 #2

    pasmith

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    Homework Helper

    [itex]\sin t \cos t = \frac12 \sin(2t)[/itex].
     
  4. Feb 28, 2015 #3
    Yea I got the answer now, thanks a lot!
     
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