Results 1 to 2 of 2

Math Help - stable/unstable DEs

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    79

    stable/unstable DEs

    Consider the differential equation given by

    y'=ay-b^2y, a>0, b>0

    List the equilibrium solutions in increasing order and classify them as stable, semistable, or unstable.

    I think I know to find the equilibrium solutions; you just factor out the y and get:

    y'=y(a-by)

    so the solutions are y=0 , y=a/b

    But how to do I see whether they're stable, unstable, or semi stable?

    any help is appreciated, thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Deadstar's Avatar
    Joined
    Oct 2007
    Posts
    722
    I'm not 101% about this but...

    Calculate the derivative of ay - by^2 and sub in the equilibrium values you found.

    If its < 0 they are stable (and in fact, a sink)

    If it's > 0 they are unstable (and a source)

    If it's = 0 we need more info.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Question about unstable equilibrium
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: May 24th 2011, 11:06 AM
  2. [SOLVED] Stable by but not Asymptotically Stable
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: September 9th 2010, 05:26 AM
  3. Equilibrium stable or unstable - differential euqation
    Posted in the Differential Equations Forum
    Replies: 20
    Last Post: July 23rd 2010, 09:34 AM
  4. Stable, but not asymptotically stable
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: February 25th 2009, 11:06 AM

Search Tags


/mathhelpforum @mathhelpforum