I am a little stuck on this problem. The question asks, Write a first order autonomous differential equation such that $y(t)=\cos(t)$ is a solution.
I understand that first order means that it contains only the first derivative of the dependent variable and autonomous means it only depends on $y$.
So $dy/dt=y(t)$ and since $\cos(t)$ is a solution $dy(t)/dt= -\sin(t)$. So the right hand side of the equation must must equal $-\sin(t)$ when $\cos(t)$ is plugged in.