In this problem you will solve the initial value problem

(1) The largest intervals that may be considered for the domain of the solution to $16 x^2 y'' - 122 x y' + 80 y = 0$ are either or .
For $-\infty$ type -inf and for $\infty$ type inf.

(2) Let $C_1$ and $C_2$ be arbitrary constants. The general solution to the homogeneous differential equation $16 x^2 y'' - 122 x y' + 80 y = 0$ is the function $y(x)=C_1\ y_1(x)+C_2\ y_2(x)=C_1$ $+C_2$ .

(3) The unique solution to the initial value problem is the function $y(x)=$ for $x \in$ .

Your overall score for this problem is