Differential equation problem

Gauss177

1. The problem statement, all variables and given/known data
a) For what nonzero values of k does the function y = sin kt satisfy the differential equation y" + 9y = 0?

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.

2. Relevant equations


3. The attempt at a solution
I'm a little confused on what I need to do here. I can do problems where you have to show that every member of a family of functions is a solution of a differential equation (differentiate the function, then plug in the function into the differential equation, and see if they are the same). But I don't see how to use that in this problem.

Thanks for the help.

cristo

Well, why not try differentiating the function, and plugging it into the equation. This will give you a condition for k such that y=sinkt is a solution.