The Auxiliary Equation for the Differential Equation $x ^ { 2 } y ^ { \prime \prime } + 3 x y ^ { \prime } + y = 6$

Multiple Choice

The auxiliary equation for the differential equation $x ^ { 2 } y ^ { \prime \prime } + 3 x y ^ { \prime } + y = 6$ is

A) $m ^ { 2 } + 3 m + 1$
B) $m ^ { 2 } + 3 m + 1 = 0$
C) $m ^ { 2 } + 2 m + 1 = 0$
D) $m ^ { 2 } + 3 m + 1 = 6$
E) $m ^ { 2 } + 2 m + 1 = 6$