Existence of a unique solution?

[bcjochim07]

Homework Statement

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
\partialf/\partialy = -1

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

 

[Dick]

Yes, f and it's partial derivative are continuous everywhere. The solution is unique.