Results 1 to 3 of 3

Math Help - Finding unique solutions

  1. #1
    Member
    Joined
    Jun 2012
    From
    Georgia
    Posts
    191
    Thanks
    25

    Finding unique solutions

    "Find an interval around x = 0 for which the given initial-value problem has a unique solution."

    (x-2)y" + 3y = x, y(0) = 0, y'(0) = 1

    How do I do this without solving the DE, which I haven't learned yet (but will soon)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    GJA
    GJA is offline
    Member
    Joined
    Jul 2012
    From
    USA
    Posts
    109
    Thanks
    29

    Re: Finding unique solutions

    Hi, phys251.

    There is an existence theorem for second order linear differential equations that goes as follows:

    Main Theorem

    Consider the Initial Value Problem (IVP)

    y''(x)+p(x)y'(x)+q(x)y(x)=g(x), y(x_{0})=y_{0} and y'(x_{0})=y_{1}.

    If the functions p(x), q(x) and g(x) are continuous on the open interval I that contains the point x_{0}, then the IVP has exactly one solution throughout the interval I.

    To start, x_{0}=0 in our example. I would suggest dividing through by x-2 and seeing if you can use the Main Theorem from there. Think about it a little more, and if you're still stuck I'll detail a little further what I had in mind for this exercise.

    Good luck!
    Last edited by GJA; August 17th 2012 at 10:32 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2012
    From
    Kunming
    Posts
    3

    Re: Finding unique solutions

    some crazy partial fractions, but I think this definitely can't be right as I'm supposed to end up with another piecewise function as my answer. Could anyone point me in the right direction? I have never done a piecewise function with functions of t as the values.
    chaussures jordan 6
    timberland bottes timberland bottes pas cher
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: October 2nd 2011, 09:33 AM
  2. Replies: 1
    Last Post: March 24th 2010, 01:14 AM
  3. unique and infinitely solutions problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 18th 2009, 07:56 PM
  4. Replies: 2
    Last Post: September 7th 2009, 03:01 PM
  5. Replies: 4
    Last Post: January 28th 2009, 02:57 PM

Search Tags


/mathhelpforum @mathhelpforum