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Math Help - differential equations

  1. #1
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    differential equations

    sketch typical solutions for the following differential equations
    indicate the set of points for which dy/dx = 0 by a dotted curve and determine the stability of any equilibria

    can someone solve one example of this in full detail so i can attempt the rest

    dy/dx = y(y-1)(y-2)
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  2. #2
    Super Member Rebesques's Avatar
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    Solve y(y-1)(y-2)=0 to get the equilibria y=0,1,2.

    To check stability say for y=0, note that
    for solutions y with initial values near 0, we have dy/dt<0,
    and so the solutions tend to the equilibrium when y>0 and diverge to infinity for y<0. Thus y=0 is unstable.
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