Using the Method of Undetermined Coefficients, Determine the Most Suitable $y _ { p }$

Multiple Choice

Using the method of undetermined coefficients, determine the most suitable choice for $y _ { p }$ given $y ^ {tt } - 3 y ^ { t } - 54 y = x ^ { 2 }$ . (You do not need to solve the differential equation.)

A) $y _ { p } = A x + B$
B) $y _ { p } = A x ^ { 2 } + B x + C$
C) $y _ { p } = A x ^ { 3 } + B x ^ { 2 } + C x + D$
D) $y _ { p } = A x ^ { 3 } + C x$
E) $y _ { n } = A x ^ { 2 }$