For what values of k does the function y = cos(kt) satisfy the differential equation 9y'' = −100y? (enter your answers as a comma-separated list.)

-10/3, 10/3

Step-by-step explanation:

(In this answer I will use y' to denote the derivative of y with respect to t. You shouldn't normally do this because y' normally means the derivative of y with respect to x but I'll be a bit messy for this case)

First calculate the derivatives:

.

Then plug the derivtes y'' and y into the equation:

Solve the equation for k:

So then we have that satisfies the differential equation when or when (or both). The solutions to these equations are:

I understand that looks a bit complicated and I doubt you would have to give your answers in terms of t so if it asks for a separated list of answers I would go for:

k = -10/3, 10/3.

d

step-by-step explanation: