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Math Help - Equilibrium solution limit to differential equation

  1. #1
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    Equilibrium solution limit to differential equation

    Can someone please help me with this one? I have found the equilibrium solutions,but I'm not sure what to do next.

    Consider dx/dt = x^3 - 4x

    Given a solution x(t) which satisfies the condition x(0) = 1, determine the limit(t -> infinity) of x(t).

    Thanks!
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  2. #2
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    Re: Equilibrium solution limit to differential equation

    Well what did you get for your solution?
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    Re: Equilibrium solution limit to differential equation

    I got the equilibrium solutions x = -2 , 2 and 0. Out out these only x = 0 is stable. Not sure where to go from here though...
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    Re: Equilibrium solution limit to differential equation

    I meant, what did you get for the solution to your DE? Hint: It's separable and can be solved using partial fractions.
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    Re: Equilibrium solution limit to differential equation

    Have you never taken a Calculus class? This is, as Prove It said, separable- it can be "separated" as
    \frac{dx}{x^3- 4x}= \frac{dx}{x(x- 2)(x+ 2)}= dt
    Integrate!
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  6. #6
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    Re: Equilibrium solution limit to differential equation

    Thank you HallsofIvy, I got the answer.

    Actually the reason I asked this question was because in the worked solutions my professor had just written:

    "If x(0) = 1 then the limit = 0"

    So I assumed there had to be a simpler way than actually solving the ODE. I was thinking maybe...would looking at the direction field suffice in this case?
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