The Auxiliary Equation for the Differential Equation $x ^ { 2 } y ^ { \prime \prime } + 5 y ^ { \prime } + 4 y = 6$

Multiple Choice

The auxiliary equation for the differential equation $x ^ { 2 } y ^ { \prime \prime } + 5 y ^ { \prime } + 4 y = 6$ is

A) $m ^ { 2 } + 5 m + 4$
B) $m ^ { 2 } + 4 m + 4 = 0$
C) $m ^ { 2 } + 5 m + 4 = 0$
D) $m ^ { 2 } + 5 m + 4 = 6$
E) $m ^ { 2 } + 4 m + 4 = 6$