$p$ is a polynomial such that $\deg(p)\geq 1$ and $p(x)>0$ whenever $x\geq 0.$ How can one show that there is no function $f$ satisfying the following two properties:
(1) $f(\frac{\pi}{2})=\frac{\pi}{2}$ and f^'(x)=\frac{1}{x^r+p(f(x))} for $x\geq \frac{\pi}{2}$ and $r>1$
(2)$\lim_{x\rightarrow \infty}f(x)=\infty$