# showing existence of nontrivial solution

Show that the differential equation $x' = \frac{x \sin(e^x+t)}{1+(e^t \cos x+x)^2}, x(1) = 1$ has a nontrivial solution $\phi(t)$ defined on
$[0,2]$ such that $0 < \phi(t) < \frac{\pi}{2}$ for all $t \in [0,2]$.