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Undetermined Coefficients, more than one term on RHS

  1. Mar 15, 2010 #1
    1. The problem statement, all variables and given/known data
    y''-49y=7cos(7x)+7+e^(7x)


    3. The attempt at a solution
    I have no idea how to solve this Differential equation. I could solve one that has y''-49y=one term, but I'm stumped with more than one.

    First, I get the homogeneous equation, y''-49y=0 and fine y_c, then use the formulas to get y_p, but that is where I'm stumped, since I'm not sure how to find it with the 3 terms on the R.H.S.
     
  2. jcsd
  3. Mar 15, 2010 #2

    rock.freak667

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    Homework Helper

    You just add the yp]'s for the individual functions.

    For example, if your RHS was ex+cosx, your yp would be
    yp=Aex+Bcosx+Csinx.
     
  4. Mar 15, 2010 #3
    Awesome. That sounds like exactly what I needed to know. Thanks!
     
  5. Mar 15, 2010 #4
    for more than one term on the right hand side you just sum up the result. i.e for 7cos(7x)
    yp=Acos(wx)+Bsin(wx). for 7 yp=C and for e^(7x) yp=De^([tex]\lambda[/tex]x)
    using sum rule yp=Acos(wx)+Bsin(wx)+C+De^([tex]\lambda[/tex]x)

    edit: guess rock beat me to it
     
  6. Mar 15, 2010 #5

    rock.freak667

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    Just be sure to note that you will have to modify your yp a bit, since '7' appears as a root in your auxiliary equation.
     
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