Find a Trial Solution for the Method of Undetermined Coefficients $y ^ { \prime \prime } + 3 y ^ { \prime } + 5 y = x ^ { 4 } e ^ { 9 x }$

Multiple Choice

Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients. $y ^ { \prime \prime } + 3 y ^ { \prime } + 5 y = x ^ { 4 } e ^ { 9 x }$

A) $y _ { y } ( x ) = \left( A x ^ { 4 } + B x ^ { 2 } + C \right) e ^ { - 9 x }$
B) $y _ { y } ( x ) = \left( A x ^ { 3 } + B x ^ { 2 } + C x + D \right) e ^ { 9 x }$
C) $y _ { y } ( x ) = \left( A x ^ { 4 } + B \right) e ^ { 9 x }$
D) $y _ { y } ( x ) = A x ^ { 9 }$
E) $y _ { y } ( x ) = \left( A x ^ { 4 } + B x ^ { 3 } + C x ^ { 2 } + D x + E \right) e ^ { 9 x }$