Question

Having trouble with the particular solution:
y''+4y'+8y=2cos(2t)+sin(2t)

Answer 1

Guess Acos(2t)+Bsin(2t)

Answer 2

I tried \[y_p=A \cos 2t+B \sin 2t\] and plugged in its derivatives, but I ended up with A=2/13 and B=3/13, but in the answer they are A=0 and B=1/4

Answer 3

Oops I the 2 in 2t when differentiating. That's probably it, gonna try it now.

Answer 4

I neglected* the 2 in 2t