ODE Existence/Uniqueness Intervals

[middleramen]

Homework Statement

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]

Homework Equations

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.

 

[Char. Limit]

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).