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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?

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