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Math Help - Differential Equation, Equalibrium

  1. #1
    Len
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    Differential Equation, Equalibrium

    Consider the Differential Equation

    \frac{dy}{dt}=2*\sqrt{|y|}

    Show that the function y(t)=0 is an equilibrium solution for all t.

    Is this simply showing the derivative of 0 is 0 and then that 2*\sqrt{|0|}=0 ? for all t because it depends on y?
    Last edited by Len; January 27th 2010 at 08:23 PM.
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    Yes. Equilibrium solutions are constant solutions to the differential equation. They can be found by simply setting the derivative equal to 0 and solving for the dependent variable. This is assuming you are looking at an autonomous differential equation, that is, one in which the independent variable does not appear ( \frac{dy}{dx} = f(y) ).

    Check here for a more thorough description: Pauls Online Notes : Differential Equations - Equilibrium Solutions
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Len View Post
    Consider the Differential Equation

    \frac{dy}{dt}=2*\sqrt{|y|}

    Show that the function y(t)=0 is an equilibrium solution for all t.

    Is this simply showing the derivative of 0 is 0 and then that 2*\sqrt{|0|}=0 ? for all t because it depends on y?
    No, an equilibrium solution is one that is unchanging, so y'(t)=0 for all t. In this case this gives:

    2\sqrt{|y|}=0

    and the rest you know.

    CB
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