Hi! Thanks for reading! :) 1. The problem statement, all variables and given/known data 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. 2. Relevant equations I just know that this excercise is under the title of "The existence and uniqueness theorem". 3. 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!