Is it possible to find a function g(y) (either continuous or discontinuous) such that th...

Is it possible to find a function g(y) (either continuous or discontinuous) such that the one-parameter family of differential equations

satisfies both of following statements?

• For all a ≤ —1, the differential equation has exactly one equilibrium point and that equilibrium is a sink.

• For all a≥1, the equation has exactly three equilibria, two of which are sources and one is a sink.

If so, sketch the graph one such g(y). If not, why not?