So this is actually a physics problem but im having problem with the math again.

My function is: y'' + y*sin(a)*k^2 = 0 , where a and k are constants.

from this I get the following solution;

y = y(max)*cos(w*t + a)

where w = sin(a)*k.

This far I understand everything. However after this my teacher has written "thus it is stable"

My question is how can he tell that it is stable? I know there is some way to do like secondary derivative tests? Can I do that or can it be seen someother way wheter its stable or not?

Looking forward to answers.