Is it possible to find a continuous function f (y) such that the one-parameter family of differential equations dy/dt = f (y)+ α satisfies both of the following statements?
• For α = 0, the differential equation has exactly one equilibrium point and that equilibrium is a sink.
• For α = 1, the equation has exactly one equilibrium point and that equilibrium is a source.
If so, sketch the graph of one such f (y). If not, why not?
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