Studying the following Cauchy problem

I have the following Cauchy problem:

$$y' = y^2 - (\arctan{x})^2$$ $$y(1) = 0$$

I want to draw a the plot of the solution.

This is what I have so far:

$$f(x,y) = y^2 - (\arctan{x})^2$$ is $$C^\infty$$ so I have Lipschizianity, therefore existence and uniqueness of local solution. It can be extended to $$\mathbb{R}$$ as a global solution.

I also know that the function is increasing when: $$\vert{y}\vert > \vert\arctan{x}\vert$$

But I am struggling to see the big picture here, how do I go on?