Consider the differential equation .(a) Show that the function y(t) = 0 for all t is an eq...

Consider the differential equation .

(a) Show that the function y(t) = 0 for all t is an equilibrium solution.

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(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.”]

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

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(d) What does HPGSolver do with this equation?