Limes for an unknown solution

1. Dec 5, 2004

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?

2. Dec 5, 2004

arildno

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

Right! That means, $$y\leq{\arctan{x}}$$, therefor the limit of y is $$\leq{\pi/2}$$.