- #1
Raziel2701
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Homework Statement
Determine the limiting behavior of solutions as t [tex]\rightarrow \infty[/tex], for all possible values [tex]y_0 = y(0)[/tex]
Homework Equations
[tex] \frac{dy}{dt}=4-y^2[/tex]
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?