Results 1 to 3 of 3

Math Help - Riccati Equation: existence/uniqueness relation

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    9

    Riccati Equation: existence/uniqueness relation

    What does the existence/uniqueness theorem say about solutions to initial value problems for Riccati equations of the form



    This is what I came up with, but I'm not sure.

    A Riccati Equation of a particular form has a unique solution satisfies the following conditions:
    It is to exist for large values of the independent variable

    Its graph must stay above a certain line for large values of the variable
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by tn2k7 View Post
    What does the existence/uniqueness theorem say about solutions to initial value problems for Riccati equations of the form



    This is what I came up with, but I'm not sure.

    A Riccati Equation of a particular form has a unique solution satisfies the following conditions:
    It is to exist for large values of the independent variable

    Its graph must stay above a certain line for large values of the variable
    First we need to isolate the derivative

    \frac{dy}{dx}=f(x,y) so we get

    f(x,y)=y'=-(y^2+1)

    Since both f(x,y) and \frac{\partial f}{\partial y} are continous on a rectnagle containing (0,1) the solution exists and is unique.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2008
    Posts
    9
    Hi, thanks for your help. I was wondering if you (or anyone else) could help me with this similar problem.

    What does the existence/uniqueness theorem say about solutions to initial value problems for Riccati equations of the form

    y'(x) + y(x)^{2} + Ay(x) + B = 0.

    Thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Existence and Uniqueness
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: February 11th 2011, 01:17 PM
  2. Quiestion to do with existence and uniqueness of a equation
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: February 15th 2010, 03:23 AM
  3. Existence and Uniqueness Th.
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: April 2nd 2009, 04:37 AM
  4. existence and uniqueness question of DFQ
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 20th 2008, 09:04 AM
  5. Existence and Uniqueness
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 16th 2007, 11:44 PM

Search Tags


/mathhelpforum @mathhelpforum