for what values of k does the function y=costkt satisfy the differential equation 4y''=-25y?
As it is, you've left only one trivial (but important) thing for the OP to do. I hope that this one small thing remains left for the OP.
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:
then I plug in the value of k and get
I'm uncertain what to do next or if the question is completed
Now, simplify the LHS to see that LHS = RHS which implies that the family of functions satisfies the differential equation.
To answer you're last question on LaTeX, click on the edited LaTeX image to see the code.