(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The theorem for a unique solution to a DE says: Let R be a rectangular region in the xy plane that contains the point (xo,yo). If f(x,y), which = dy/dx and the partial derivative of f(x,y) are continuous on R, then a unique solution exists in that region.

Question: Determine a region of the xy plane for which the given differential equation would have a unique solution.

dy/dx= x-y

dy/dx= f(x,y)= x-y ,so f(x,y) is continuous on all reals for x & y

then

[tex]\partial[/tex]f/[tex]\partial[/tex]y = -1

So this means that the solution is unique everywhere, right?

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# Homework Help: Existence of a unique solution?

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