Solve the Differential Equation $y ^ {tt} - 6 y ^ { t } + 9 y = 8 x ^ { 2 } e ^ { 3 x } \text { by the method of variation of }$

Multiple Choice

Solve the differential equation $y ^ {tt} - 6 y ^ { t } + 9 y = 8 x ^ { 2 } e ^ { 3 x } \text { by the method of variation of }$ parameters.

A) $y = \left( C _ { 1 } + C _ { 2 } x + \frac { 2 } { 3 } x ^ { 4 } \right) e ^ { 3 x }$
B) $y = \left( C _ { 1 } + C _ { 2 } x + \frac { 8 } { 15 } x ^ { 4 } \right) e ^ { 3 x }$
C) $y = \left( C _ { 1 } + C _ { 2 } x + \frac { 4 } { 9 } x ^ { 2 } \right) e ^ { 3 x }$
D) $y = \left( C _ { 1 } + C _ { 2 } x - \frac { 8 } { 17 } x ^ { 2 } \right) e ^ { 3 x }$
E) $y = \left( C _ { 1 } + C _ { 2 } x - \frac { 4 } { 5 } x ^ { 2 } \right) e ^ { 3 x }$