Find the Particular Solution of the Given Differential Equation That $\frac { d y } { d x } - y = 2 x ^ { 2 } ; y = 1 \text { when } x = 3$

Multiple Choice

Find the particular solution of the given differential equation that satisfies the given condition. $\frac { d y } { d x } - y = 2 x ^ { 2 } ; y = 1 \text { when } x = 3$

A) $y = \frac { 35 e ^ { x - 3 } } { x ^ { 2 } + 2 x + 2 }$
B) $y = 35 e ^ { x - 3 } - 2 \left( x ^ { 2 } + 2 x + 2 \right)$
C) $y = 35 e ^ { x } + 2 \left( x ^ { 2 } + 2 x + 2 \right)$
D) $y = C e ^ { x - 3 } - 2 \left( x ^ { 2 } + 2 x + 2 \right)$