Results 1 to 2 of 2

Math Help - Depict graphically the flow of the following equation...

  1. #1
    Junior Member
    Joined
    Apr 2007
    Posts
    32

    Depict graphically the flow of the following equation...

    If you have dx/dt = (x-2)(x-3)^2.


    I know how to do the flow diagram and it has equilibrium points at x=2 (unstable) and x=3 (semi-stable?).

    But am confused about this:

    Describe the behaviour of x(t) as t -> infinity for different initial values x(0) = x0.

    What do you do for this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Rebesques's Avatar
    Joined
    Jul 2005
    From
    At my house.
    Posts
    538
    Thanks
    11
    So you have x'=(x-2)(x-3)^2. We see that

    x'\begin{cases}<0, \ x<2 \\ >0, \ x>2 \end{cases}

    and thus: For x(0)=x_0<2, the solution flows away from x=2 to minus infinity. For x(0)=x_0\in(2,3), the solution flows away from x=2 and tends to x=3. And for x(0)=x_0>3, the solution flows away from x=3 to infinity.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: March 9th 2012, 09:08 AM
  2. A flow map in differential equations (not a flow chart)
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: October 23rd 2010, 04:01 PM
  3. Replies: 2
    Last Post: September 9th 2009, 08:15 PM
  4. Couette Flow differential equation
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: November 2nd 2008, 03:58 PM
  5. differencial equation of flow
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 30th 2008, 07:29 AM

Search Tags


/mathhelpforum @mathhelpforum