Consider the initial value problem
$$(8t^2 - 45t + 25) y'' - 3.5ty = \sin(0.5\pi t), y\left(\frac{45}{16}\right) = -3, y'\left(\frac{45}{16}\right) = 3.5.$$
On which of these intervals is this initial value problem certain to have a unique twice differentiable solution? Select all that apply.
$$(-\infty, \infty)$$
$$(0, 5)$$
$$\left(\frac{5}{8}, 5\right)$$
$$(-3, 3.5)$$
$$\left(\frac{55}{32}, \frac{125}{32}\right)$$
