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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

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    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).
     
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