First rearrange the equation:
x = 2y then 2y = x y= 1/2x
So the slope is 1/2
Answer:
D
Step-by-step explanation:
The open circle at the origin means the rightmost piece will have domain x > 0. That is only the case in choices C and D.
The middle piece has a negative slope. That is only the case in choice D.
The appropriate piecewise function is ...

Explanation:
Differentiating the solution, we have ...
y' = c1 +8c2x^7
y'' = 56c2x^6
Putting this into the DE, we have ...
x^2y'' -8xy' +8y = 16 . . . . . . . different from your problem statement
x^2(56c2x^6) -8x(c1 +8c2x^7) +8(c1x +c2x^8 +2) = 16
56c2x^8 -8c1x -64c2x^8 +8c1x +8c2x^8 +16 = 16
x^8(56c2 -64c2 +8c2) +x(-8c1 +8c1) +16 = 16
0 +16 = 16 . . . . QED
The smallest number of the group is .103