Results 1 to 6 of 6
Like Tree1Thanks
  • 1 Post By chiro

Math Help - Show that the initial value problem has a solution on R.

  1. #1
    Junior Member
    Joined
    Dec 2011
    Posts
    57
    Thanks
    1

    Show that the initial value problem has a solution on R.

    Show that the initial value problem x' = \frac{{x^3}{e^{t}}}{1+x^2} + {t^2}{\cos x}, x(0) = 1 has a solution on \mathbb{R}.


    I tried to use Picard's theorem, but to no avail I can't get any result.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,612
    Thanks
    591

    Re: Show that the initial value problem has a solution on R.

    Hey alphabeta89.

    It's been a while since I did DE's, but have you heard of the Lipschitz condition for the existence of a solution for a particular DE?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2011
    Posts
    57
    Thanks
    1

    Re: Show that the initial value problem has a solution on R.

    Nope, how do I go about doing it?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,612
    Thanks
    591

    Re: Show that the initial value problem has a solution on R.

    I haven't watched the video myself, but you might want to look at this:

    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Dec 2011
    Posts
    57
    Thanks
    1

    Re: Show that the initial value problem has a solution on R.

    Ok, so which domain of t and x do I apply on?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,612
    Thanks
    591

    Re: Show that the initial value problem has a solution on R.

    Well you have a positive period of L so you can think about the circle going from 0 to 2pi and the other object going from 0 to L.
    Thanks from alphabeta89
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding a solution given initial value problem
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: September 22nd 2012, 01:04 PM
  2. Existence of a solution; Initial value problem
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: December 3rd 2010, 11:35 PM
  3. series solution of an initial value problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 27th 2010, 09:52 AM
  4. Replies: 3
    Last Post: February 16th 2008, 03:58 PM
  5. Replies: 3
    Last Post: April 23rd 2007, 06:08 PM

Search Tags


/mathhelpforum @mathhelpforum