In this problem you will solve the initial value problem $$x^2 y'' + 6 x y' + 6 y =0,\ \ y(-1) = -7,\ \ y'(-1) = 6.$$

(1) The largest intervals that may be considered for the domain of the solution to $x^2 y''+ 6 x y' + 6 y = 0$ 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 $x^2 y''+ 6 x y' + 6 y = 0$ 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 $$x^2 y''+6 x y' + 6 y =0,\ \ y(-1) = -7,\ \ y'(-1) = 6.$$ is the function $y(x)=$ for $x \in$ .