(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine the limiting behavior of solutions as t [tex]\rightarrow \infty[/tex], for all possible values [tex]y_0 = y(0)[/tex]

2. Relevant equations

[tex] \frac{dy}{dt}=4-y^2[/tex]

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

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

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