Find the Solution to the Differential Equation $x y ^ { \prime } - ( 6 + x ) y = 0$

Multiple Choice

Find the solution to the differential equation $x y ^ { \prime } - ( 6 + x ) y = 0$ with $y ( 1 ) = 1$ , $y ( x ) \geq 0$ for all x.

A) $y = x ^ { 7 } e ^ { x }$
B) $y = x ^ { 7 } e ^ { x - 1 }$
C) $y = x ^ { 6 } e ^ { x - 1 }$
D) $y = x ^ { 6 } e ^ { x } + 1 - e$