Originally Posted by
superdude yes I did get that answer, plus or minus 5/2
part b) I'm stuck on again. "For those values of k, verify that every member of the family of functions y=Asinkt+Bcoskt is also a solution." (where A,B, and of course k, are constants). This is what I did:
$\displaystyle \begin{aligned}
y & = A\sin(kt)+B\cos(kt)\\
y' & =Ak\cos(kt)-bk\sin(kt)\\
y'' & =-Bk^2\cos(kt)-Ak^2\sin(kt)\end{aligned}
$
then I plug in the value of k and get
$\displaystyle
4(\frac{-25b\cos(5t/2)}{4}-\frac{25a\sin(5t/2)}{4})=-25b\cos(5{\color{red}t}/2)-25a\sin(5{\color{red}t}/2)
$
I'm uncertain what to do next or if the question is completed
I'm sorry, how do I cause a line break with latex?