1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

ODE Existence/Uniqueness Intervals

  1. Feb 12, 2013 #1
    1. The problem statement, all variables and given/known data

    Obtain intervals x∈[0,α] for the existence of a unique solution

    dy/dx = f(x,y) = e^-(y-x)^2; y(0) = 0

    on the rectangle B = [0,a]x[-b,b]

    2. Relevant equations

    3. The attempt at a solution

    Since both dy/dx and it's partial derivative of y are both continuous, a unique solution exists. Thus an interval for existence for t is [0,t*], where t* = b/(max|f(x,y)|).

    I'm not sure how to determine max|f(x,y)|.

    Any help is appreciated.
    Last edited: Feb 12, 2013
  2. jcsd
  3. Feb 12, 2013 #2

    Char. Limit

    User Avatar
    Gold Member

    f(x,y) = e^(- (y-x)^2), correct? In that case, it seems to me that it would be easier to temporarily define a new variable, say, p = y-x, and substitute that in. From there, it's easy to find the maximum value of e^(-p^2).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook