Consider the Initial Value Problem

on Which of These $(0,2 \pi)$

Multiple Choice

Consider the initial value problem

On which of these intervals is this initial value problem certain to have a unique twice differentiable solution? Select all that apply.

A) $(0,2 \pi)$
B) $(-2 \pi, 2 \pi)$
C) $(0, \infty)$
D) $\left(\frac{\pi}{12}, \frac{5 \pi}{4}\right)$
E) $\left(0, \frac{\pi}{12}\right)$
F) $\left(-\frac{5 \pi}{4}, \frac{5 \pi}{8}\right)$