1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook