How Does the Solution of y' = 1/(1+x^2+y^2) Behave as x Approaches Infinity?

[Zaare]

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

 

[arildno]

For ALL x, you have:
$$0\leq{y'}\leq\frac{1}{1+x^{2}}$$

How does this help you?

 

[Zaare]

Right! That means, $$y\leq{\arctan{x}}$$, therefor the limit of y is $$\leq{\pi/2}$$.
Thanks. I appreciate the help. :)