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Differential Equations: Second Order Equations

  • Thread starter peace-Econ
  • Start date
  • #1
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Homework Statement



find a particular solutions for the given differentiable equation.

Homework Equations



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

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!
 

Answers and Replies

  • #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?
 
  • #3
34
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yea, I realized that, but I don't kno what's missing...that's a problem.
 
Last edited:
  • #4
209
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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.
 
  • #5
34
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I already tried y=at^2+bt+c, but I still didn't have a way t cancel out t...
 
  • #6
34
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Oh, wait! I don't have to cancel out t...!lol I was too stupid...
 

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