Results 1 to 2 of 2

Thread: differential equations

  1. #1
    Jan 2009

    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)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Rebesques's Avatar
    Jul 2005
    My house.
    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.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. 'Differential' in differential equations
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: Oct 5th 2010, 10:20 AM
  2. Replies: 2
    Last Post: May 18th 2009, 03:49 AM
  3. Replies: 5
    Last Post: Jul 16th 2007, 04:55 AM
  4. Replies: 3
    Last Post: Jul 9th 2007, 05:30 PM
  5. Differential equations
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Feb 14th 2007, 04:29 PM

Search Tags

/mathhelpforum @mathhelpforum