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

  1. Jan 25, 2010 #1
    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
     
  2. jcsd
  3. Jan 25, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    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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