Results 1 to 2 of 2

Math Help - Why ode solution tends to a constant?

  1. #1
    Junior Member
    Joined
    Jun 2011
    Posts
    73
    Thanks
    2

    Why ode solution tends to a constant?

    Problem 2 Consider an autonomous system of differential equations





    where is a vector field.
    1. Let and be two solutions on . Assuming that



      for all x, z in , show that is a decreasing function of .
    2. Let be a solution defined for . Assuming that



      show that there exists such that

    Would someone help me in the second question? I have no idea about it.

    PS: This is Berkely math problem Fall 81, Problem 2.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2

    Re: Why ode solution tends to a constant?

    I don't know about others, but all your pictures are broken. Please fix.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Why bounded ode solution tends to a constant
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: October 16th 2011, 07:32 PM
  2. No solution for an arbitrary constant.
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: April 1st 2011, 05:41 AM
  3. Particular Solution for Constant Coefficients ODE
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: February 26th 2011, 10:57 AM
  4. Constant(?) Solution of a Separable ODE.
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: May 22nd 2010, 04:02 PM
  5. Finding a Solution using an integrating constant
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: January 13th 2010, 05:41 AM

Search Tags


/mathhelpforum @mathhelpforum