Differential equation nonzero value problem

[Gauss177]

Homework Statement

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.

Homework Equations

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.