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Guessing the particular solution

  1. Oct 24, 2015 #1
    1. The problem statement, all variables and given/known data
    Find both a particular solution yp (via the method of educated guess) and a general solution y.
    y(2)-6y(1)=25sin(6x)


    2. Relevant equations


    3. The attempt at a solution
    This was my guess:
    yp(x)=Asin(6x)
    I then took derivatives, plugged them in, and simplified to get this:
    -27Asin(6x)-36Acos(6x)=25sin(6x)
    I'm stuck at this point! How do I solve for A? Or did I just make a bad guess for the particular solution?
     
  2. jcsd
  3. Oct 24, 2015 #2
    you end up with sin and cos terms, so it makes sense to try as particular solution also something with sin and cos terms:
    [itex]y_p = A\sin(6x) + B\cos(6x)[/itex]
     
  4. Oct 24, 2015 #3
    Ohhhh duh, thanks so much!
     
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