anonymous
  • anonymous
find form of a particular solution of the follow equation.. y''+11'+24y=6sin(3t)e^-8t
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
What is meant by 11'
anonymous
  • anonymous
oops, equation should be as follow \[y''+11y'+24y=6\sin(3t)^{-8t}\]
anonymous
  • anonymous
So you want to find the homogenous solution first to ensure that when you are trying to find a particular solution, you don't get any repeated solutions. Then I would probably use the method of undetermined coefficients if I were solving. Normally for sin(t) the particular solution looks something like Asin(t)+Bcos(t).

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anonymous
  • anonymous
I just need to find form, don't need to solve it or anything Roots are as follow r1=-8 and r2=-3 so \[Yc=C1e ^{-8t}+C2e ^{-3t}\] and \[Yp=(Acoos(3t)+Bsin(3t))^{-8t} is wrong?\]
anonymous
  • anonymous
I would have the -8t exponent on both sin and cos, separately not the quantity.

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