For the ODE:

y' = sin y

(a) Find the equilibrium points y* corresponding to constant solutions y(t) = y*.

(b) Plot the vector field for this ODE on the real line in y. Identify the equilibrium points

and state whether they are stable or unstable.

(c) Sketch the solutions y(t) as a function of t.

(d) Using the condition on f'(y) discussed in class, determine the stability of the equilibrium points directly and compare with your determinations in part (b).