Sketch the graph of a function f (y) such that the one-parameter family of differential equations dy/dt = f (y) + α satisfies all of the following properties:
• For all α ≤ −3, the differential equation has exactly two equilibria.
• For all α ≥ 3, the equation has no equilibria.
• For α = 0, the equation has exactly four equilibria.
[There are many possible functions f (y) that satisfy these conditions. Sketch just one graph.]
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