Let $f:[1,\infty)\to\mathbb R$ be a twice differentiable function such that $$ f'(x)=\frac{1}{x^2 + y^2} $$ and $f(1)=1$ then prove that $$ f(x)<1+\frac{\pi}{4} $$ for every $x \geqslant 1$.
My process:
I am not able to use the given differential equation as I don't know how to do it. If you can help me how to use the differential equation,I think then I can manage to solve this question.