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Find the general solution for a nonhomogenous equation.

  1. Jun 26, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the general solution for a nonhomogenous equation.
    y''+4y=3csc2t


    2. Relevant equations



    3. The attempt at a solution
    I simplified the equation to...
    y''+4y=(3)/(sin(2t))

    Then I guessed...
    y=Asint+Bcost
    y'=Acost-Bsint
    y''=-Asint-Bcost


    Then I got...
    -Asint-Bcost+4Asint+4Bcost=(3)/(sin(2t))

    Simplifies to...
    3Asint+3Bcost=(3)/(2sintcost))

    NOTE: Trig Identity: sin(2t)=2sintcost

    I am stuck and I am not even sure if I took the correct steps.
     
    Last edited: Jun 26, 2011
  2. jcsd
  3. Jun 26, 2011 #2

    hunt_mat

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    Variations of parameters.
     
  4. Jun 26, 2011 #3
    Thanks for your help! I have been trying to figure out Variation of Parameters and I can't seem to find it on Khan Academy. Any chance there are any videos or resources you can suggest?
     
  5. Jun 26, 2011 #4

    rock.freak667

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    http://en.wikipedia.org/wiki/Variation_of_parameters" [Broken] is always a good place as sometimes they'll give an example...like in what I posted.
     
    Last edited by a moderator: May 5, 2017
  6. Jun 26, 2011 #5
  7. Jun 26, 2011 #6
    Thanks for everyone's help! I got a solution, although it kinda looks weird, but it makes sense to me now! :)
     
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