What am I doing wrong? Integration and limits I need some help identifying what I'm doing wrong here..
What is the limit of $y(x)$ when $x→∞$ if $y$ is given by:
$$y(x) = 10 + \int_0^x \frac{22(y(t))^2}{1 + t^2}\,dt$$
What i've done:
1) Integrating on both sides(and using the Fundamental Theorem of Calculus):
$$\frac{dy}{dx} = 0 + \frac{22(y(x))^2}{1 + x^2}$$
2)
$$\frac{-1}{22y} = \arctan x$$
And after moving around and stuff I end up with the answer:  $\quad\dfrac{-1}{11 \pi}.$
What's wrong?

Here is how you finish your problem. You are missing the constant of integration
$$ -\frac{1}{y(x)}= \tan^{-1}(x) +c. $$
Now, use the initial condition $y(0)=10$ to find $c$ then you will be able to find the limit.
