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Homework Help: ODE - having trouble using method of undetermined coefficients

  1. Sep 20, 2011 #1
    1. The problem statement, all variables and given/known data

    Find a particular solution.
    1. y'' +4y = 4 cos (2t) (for this problem, the instructions tell me that the forcing term is a solution of the associated homogeneous solution)
    2. y'' + 16 y = 3 sin (4t)


    2. Relevant equations



    3. The attempt at a solution
    1. I guess that Acos (2t) + Bsin (2t) was a solution but it did not work out. I am thinking that since the roots to the characteristic polynomial are 2i with a multiplicity of two this means that a basis for the homogeneous solution space is { cos (2t) + sin (2t) , t cos (2t) + t sin (2t)}. So I am thinking a better guess should be A t^2 cos (2t) + B t^2 sin (2t). Is this correct?
    2. For this one I guessed Acos (4t) + Bsin (4t) was a solution but it did not work out (provided that I did my computation correctly). Any suggestions?


    Thanks!
     
  2. jcsd
  3. Sep 20, 2011 #2
    1) The characteristic equation is

    [tex]r^2 + 4 = 0 [/tex]

    2i is not a multiplicity of 2...
     
  4. Sep 20, 2011 #3
    since your ODE does not have y' term, what would be a better guess?

    hint:
    y=Acos(4t)
    y''=-Acost(4t)
     
  5. Sep 20, 2011 #4
    If I choose y =A cos (2t) Then wouldn't y'' = -4 A cos (2t) and then y'' + 4 y = 0
     
  6. Sep 20, 2011 #5
    I figured it out
     
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