For what $\displaystyle nonzero$ values of $\displaystyle k$ does the function $\displaystyle y=sinhkt$ satisfy the DE $\displaystyle y''-25y=0$?

I got $\displaystyle k=5$ and $\displaystyle k=-5$ which I think is correct, but I'm struggling with the other two parts of the question:

For those values of $\displaystyle k$, show that every member of the family of functions $\displaystyle Asinhkt+Bcoshkt$ (where$\displaystyle A$ and $\displaystyle B$ are constants) is also a solution of the DE.

Come up with a second order DE for which $\displaystyle y=sinkt$ is a solution for the same values of $\displaystyle k$ obtained before.