Solve the Differential Equation $144 y ^ {tt} - 24 y ^ { t } + y = 12 \left( x + e ^ { x } \right) \text { by the method of }$

Multiple Choice

Solve the differential equation $144 y ^ {tt} - 24 y ^ { t } + y = 12 \left( x + e ^ { x } \right) \text { by the method of }$ undetermined coefficients.

A) $y = \left( C _ { 1 } + C _ { 2 } x \right) e ^ { 1 / 2 x } + 288 + 12 x + \frac { 12 } { 121 } e ^ { x }$
B) $y = \left( C _ { 1 } + C _ { 2 } x \right) e ^ { 1 / 12 x } + 288 + 13 x + \frac { 12 } { 121 } e ^ { x }$
C) $y = \left( C _ { 1 } + C _ { 2 } x \right) e ^ { 1 / 12 x } + 288 + 5 x + \frac { 12 } { 121 } e ^ { x }$
D) $y = \left( C _ { 1 } + C _ { 2 } x \right) e ^ { 1 / 12 x } + 288 + 12 x + \frac { 12 } { 121 } e ^ { x }$
E) $y = \left( C _ { 1 } + C _ { 2 } x \right) e ^ { 1 / 2 x } + 288 + 2 x + \frac { 12 } { 121 } e ^ { x }$