Consider the two differential equations

each having the critical points a, b, and c; suppose that a < b < c. For one of these equations, only the critical point b is stable; for the other equation, b is the only unstable critical point. Construct phase diagrams for the two equations to determine which is which. Without attempting to solve either equation explicitly, make rough sketches of typical solution curves for each. You should see two funnels and a spout in one case, two spouts and a funnel in the other.

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and dx dt dx dt = (x - a)(x - b)(x-c) (a-x)(b - x)(c-x), (21) (22)