Homework Help: Determine limiting behavior as t goes to infinity(Differential Equation)

1. Jan 25, 2010

Raziel2701

1. The problem statement, all variables and given/known data
Determine the limiting behavior of solutions as t $$\rightarrow \infty$$, for all possible values $$y_0 = y(0)$$

2. Relevant equations

$$\frac{dy}{dt}=4-y^2$$

3. The attempt at a solution

I've obtained the constant solutions, they are -2 and 2. I sketched dy/dt to determine the monotonicity, and found that the constant solution 2 is stable. My question is whether this stable solution is what determines the behavior as t goes to infinity.

I just started taking differential equations and I'm trying to get used to the language and the nature of the questions. Since 2 is a stable solution, that should mean that all initial values of y should go to 2 as time passes correct?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 25, 2010

Dick

No. A solution doesn't have to approach the stable solution unless it starts out near the stable solution. Otherwise, it might just go to infinity.

Last edited: Jan 25, 2010
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