find form of a particular solution of the follow equation.. y''+11'+24y=6sin(3t)e^-8t

Question

anonymous · Answer

What is meant by 11'

anonymous · Answer

oops, equation should be as follow $$y''+11y'+24y=6\sin(3t)^{-8t}$$

anonymous · Answer

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).

anonymous · Answer

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 · Answer

I would  have the -8t exponent on both sin and cos, separately not the quantity.