Discuss the existence and uniqueness of a solution to the differential equation $(4+t^2)y'' + ty' - y = \tan t$ that satisfies the initial conditions $y(3) = Y_0$, $y'(3) = Y_1$, where $Y_0$ and $Y_1$ are real constants.\
Select the correct choice below and fill in any answer boxes to complete your choice.\
A. A solution is guaranteed only at the point $t_0 = $ because the functions $p(t) = $, $q(t) = $, and $g(t) = $ are simultaneously defined at that point.\
B. A solution is guaranteed on the interval $\boxed{\hspace{0.5cm}} < t < \boxed{\hspace{0.5cm}}$ because it contains the point $t_0 = \boxed{\hspace{0.5cm}}$ and the functions $p(t) = \boxed{\hspace{0.5cm}}$, $q(t) = \boxed{\hspace{0.5cm}}$, and $g(t) = \boxed{\hspace{0.5cm}}$ are equal on the interval.\
C. A solution is guaranteed on the interval $\boxed{\hspace{0.5cm}} < t < \boxed{\hspace{0.5cm}}$ because it contains the point $t_0 = \boxed{\hspace{0.5cm}}$ and the functions $p(t) = \boxed{\hspace{0.5cm}}$, $q(t) = \boxed{\hspace{0.5cm}}$, and $g(t) = \boxed{\hspace{0.5cm}}$ are simultaneously continuous on the interval.
