Chapter 1.7, Problem 16E

Sketch the graph of a function g(y) such that the one-parameter family of differential equations dy/dt = g(y) + $\alpha$ satisfies all of the following properties:
• For all $\alpha \le -4$ , the differential equation has exactly two equilibria.
• For all $\alpha \ge 4$ , the equation has no equilibria.
• For $\alpha =0$ , the equation has exactly four equilibria.
[There are many possible functions g(y) that satisfy these conditions. Sketch just one graph.]