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Differential Equations: Second Order Equations

  1. Aug 12, 2011 #1
    1. The problem statement, all variables and given/known data

    find a particular solutions for the given differentiable equation.

    2. Relevant equations

    y''+5y'+6y=4-t^2

    3. The attempt at a solution

    Because the right-hand side is a polynomial of degree 1, so I want to have a particular solution of the same form. It's like y=a(t^2)+b, but if so, I kinda stuck in the middle of calculation. 6a=-1 (this is fine) and 2a+10at+6b=4 (I want to take out t). i need to use this technique. Please help me find what's wrong here.

    Thank you so much!
     
  2. jcsd
  3. Aug 12, 2011 #2
    it seems that your original guess at the particular solution is a bit lacking. your choice for y(t) is missing something... can you guess what it is missing?
     
  4. Aug 12, 2011 #3
    yea, I realized that, but I don't kno what's missing...that's a problem.
     
    Last edited: Aug 12, 2011
  5. Aug 12, 2011 #4
    You should guess y=at2+bt+c, and I'll even tell you why.

    Let y=at2+b

    If you plug that into y''+5y'+6y, you get:

    2a +5(2at) +6(at2+b) = 4-t2

    Now you nothing with which to cancel out that 10at in the middle of the left side.
     
  6. Aug 12, 2011 #5
    I already tried y=at^2+bt+c, but I still didn't have a way t cancel out t...
     
  7. Aug 12, 2011 #6
    Oh, wait! I don't have to cancel out t...!lol I was too stupid...
     
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