Consider the differential equation dy/dt = 2 √ |y|. (a) Show that the function y(t) = 0 for all t is an equilibrium solution.

(b) Find all solutions. [Hint: Consider the cases y > 0 and y < 0 separately. Then you need to define the solutions using language like "y(t) = . . . when t ≤ 0 and y(t) = . . . when t > 0."]

(c) Why doesn’t this differential equation contradict the Uniqueness Theorem?

(d) What does HPGSolver do with this equation?