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Limes for an unknown solution

  1. Dec 5, 2004 #1
    I have this eq.:
    [tex]y'=\frac{1}{(1+x^2+y^2)}[/tex]
    I'm able to show that it has a unique solution for [tex]-\infty<x<\infty[/tex], and that the solution is an odd funktion.
    What can I say about the limit of the solution as x grows towards infinity?
     
  2. jcsd
  3. Dec 5, 2004 #2

    arildno

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    For ALL x, you have:
    [tex]0\leq{y'}\leq\frac{1}{1+x^{2}}[/tex]

    How does this help you?
     
  4. Dec 5, 2004 #3
    Right! That means, [tex]y\leq{\arctan{x}}[/tex], therefor the limit of y is [tex]\leq{\pi/2}[/tex].
    Thanks. I appreciate the help. :)
     
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