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?