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

Multiple Choice

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

A) $y _ { y } ( x ) = \left( A x ^ { 4 } + B x ^ { 2 } + C \right) e ^ { - 5 x }$
B) $y _ { y } ( x ) = \left( A x ^ { 4 } + B x ^ { 3 } + C x ^ { 2 } + D x + E \right) e ^ { 5 x }$
C) $y _ { y } ( x ) = \left( A x ^ { 3 } + B x ^ { 2 } + C x + D \right) e ^ { 5 x }$
D) $y _ { y } ( x ) = A x ^ { 5 }$
E) $y _ { y } ( x ) = \left( A x ^ { 4 } + B \right) e ^ { 5 x }$