quick derivation check...

Question

anonymous · Answer

using equation tool now....

anonymous · Answer

$$y=Acos3t+Bsin3t$$
$$y'=cos3t-3Asin3t+sin3t+3Bcos3t$$
$$y''=-3sin3t-3sin3t-9Acos3t+3cos3t+3cos3t-9Bsin3t$$

anonymous · Answer

I know some terms can be combined but just checking the derivation

bahrom7893 · Answer

Where did that Cos3t in the front come from?

bahrom7893 · Answer

and the Sin3t

anonymous · Answer

ah they should just be -sin huh I used product rule with the A which is a constant :/

psymon · Answer

Aren't A and B just constants? These are problems where you are taking guesses, correct? If your guess was simply Acos3t + Bsin3t, then you dont even need product rule. Just -3sin3t + 3cos3t and then -9cos3t - 9sin3t

bahrom7893 · Answer

A and B are just constants, you don't need the product rule there.

psymon · Answer

Forgot to keep A and B in there, sorry, but still same point.

bahrom7893 · Answer

The only variable is t

bahrom7893 · Answer

(i think)

anonymous · Answer

so it should be
$$y'=-3sin3t+3cos3t$$
$$y''=-9cos3t-9sint$$

psymon · Answer

Bingo, just remembering to keep A and B in there.

anonymous · Answer

oops -9sin3t

psymon · Answer

Now you can plug your guess into the D.E and see what ya get.

anonymous · Answer

ok yeah cause that's what im solving for lol

psymon · Answer

Figured as much. Been staring at the D.E stuff in prep for my class. Good luck with the question. I have confidence it's the correct guess xD

anonymous · Answer

@Psymon  got the ans! thanks again for helping!

psymon · Answer

Awesome job ^_^