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A DFQ problem.

  1. May 26, 2008 #1
    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?
  2. jcsd
  3. May 26, 2008 #2


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    Staff Emeritus
    Science Advisor

    First, what is "Y(x)'s definition zone"?

    Second, can you put upper and lower bounds on y' in that zone?
  4. May 26, 2008 #3
    I think Y(x)'s definition zone is all of R, since Lipschitz law is being satisfied in every closed area in R^2, etc...

    Well, I can see that y'(x)<=y-1, but I can't see where it leads....
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