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Undetermined Coefficients to solve

  1. Mar 18, 2009 #1
    Undetermined Coefficients to solve.

    y'''-6y''=3-cosx

    So I set everything up, get my system & I get an answer of

    y=c1+c2x+c3e^(6x)-6/37cosx+1/37sinx

    the book has y=c1+c2x+c3e^(6x)-6/37cosx+1/37sinx-1/4x^2.

    So I'm not sure where the book gets the last term, any ideas?
     
  2. jcsd
  3. Mar 18, 2009 #2

    gabbagabbahey

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    The book's answer is correct, but I have no idea where you are going wrong since you haven't shown your work...
     
  4. Mar 18, 2009 #3
    Ok, I have yp= A + B cosx + c sinx
    y'p=-Bsinx+C cosx
    y''p=-B cosx - C sinx
    y'''P=Bsinx - C cosx

    After I have plugged these back into the LHS, I get a system of
    B+6C=0
    6B-C=-1

    These give me my coefficients -6/37cosx & 1/37sinx.
     
  5. Mar 18, 2009 #4
    Oh & yh=r^2(r-6), which is where I get c1+c2x+c3e^6c.
     
  6. Mar 18, 2009 #5

    gabbagabbahey

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    Well that's your problem right there, the constant term 'A' is not linearly independent to your homogeneous solution, which also contains a constant term.... to account for the constant term (3) on the RHS of your DE, you need to add a term of the form Ax^r where r is the smallest non-negative integer such that no terms of the same order are present in your homogeneous solution....

     
  7. Mar 18, 2009 #6
    Thanks. It works out nicely now.
     
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