The question I am stuck on is:
Find a particular solution to
$y'' + 36y = 36\sin(6t)$
I guessed that $y_p(t)$ would be $A\sin(6t)$, because I would be taking the derivative twice, so cosine would not come into play. So I used the method of undetermined coefficients to try and find $A$. However, I hit a bit of a roadblock.
When I went through my math, I got:
$$-36A\sin(6t) + 36A\sin(6t) = 36\sin(6t).$$
A can't be zero as far as I can tell.
I'm wondering what the answer would be for such a case (if this is even a special case) or if I did something wrong in my math.
Thank you in advance for any help you can give.