For what values of k does the function y $=$ cos$($kt$)$ satisfy the differential equation

$36$y$\text{'}\text{'}=25$y$?$

$($Enter your answers as a comma$-$separated list.$)$

k $=$

$($b$)$ For those values of k$,$ verify that every member of the family of functions

y $=$ A sin$($kt$)+$ B cos$($kt$)$

is also a solution.

y $=$ A sin$($kt$)+$ B cos$($kt$)$ y$\text{'}=$ Ak cos$($kt$)$ Bk sin$($kt$)$ y$\text{'}\text{'}=$Ak$2$ sin$($kt$)$ Bk$2$ cos$($kt$).$