Given: $y(x)$ is defined for $x \geq 1$ and satisfies $y'=\frac{1}{x^2+y^2}, y(1)=1$
Show that $ y(x) < \frac{5\pi}{4} $ for all $x \geq 1$
I don't see an easy way to solve for $y(x)$, and I don't know how to demonstrate that the function is always less than $5\pi/4$ without solving for $y(x)$. Any suggestions on how to approach this?