Could you please explain how to solve this question? Stable equilibrium solution

Question

Could you please explain how to solve this question?

Stable equilibrium solution is C=2. And Unstable equilibrium solutions are C=0, 0.5.

So, I thought that C will approach C=2 (stable equilibrium) as t goes infinity.

But the answer says C will approach 0.5 (unstable equilibrium).

When the question asks what will happen to the value of C as t goes infinity, whether equilibrium that is close to the point C=.17 is stable or not does not matter?

We can say it will approach 0.5 even though 0.5 is an unstable equilibrium solution?

6 points] Consider the differential equation where f(C) is the function graphed below. dC dt f(C) f(C) 3 0.25 0.50.75 1.25 15 1.752 a. [2 points Suppose that a solution to this differential equation passes through a point with C-0.17. For this solution, what will happen to the value of C asto?

Explanation / Answer

You are wrong about the equilibrium points.

C=0.5 is a stable equilibrium position

C=0 and C=2 is unstable equilibrium position

For example:

Let us take a ball, if you put the ball at a point close to 0/2 or at 0/2 it will go in the same direction no matter whether u put the ball in right side or left side of 0/2.But if you put the ball near 0.5 it will always go back to point 0.5, hence 0.5 is a stable equilibrium.

Now it is clear from the question that C will approach value 0.5 as t goes to infinity

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