# A DFQ problem.

## Homework Statement

Y(x) is the solution of the next DFQ problem:
y' = [(y-1)*sin(xy)]/(1+x^2+y^2), y(0) = 1/2.
I need to prove that for all x (in Y(x)'s definition zone), 0<Y(x)<1.

## Homework Equations

I just know that this excercise is under the title of "The existence and uniqueness theorem".

## The Attempt at a Solution

I'm sorry to say I don't have much to show here. I just noticed that for y=0, y'=0, and for y=1, y'=0... but I can't progress any farther...
Moreover, I don't see how this excercise is relevant to the existence and uniqueness theorem, but it has to be...

Hints? Tips? Anything?
Thanks!

HallsofIvy