Solve the differential equation using the method of variation of parameters. $y ^ { \prime \prime } + 4 y ^ { \prime } + 4 y = \frac { e ^ { - 2 x } } { x ^ { 3 } }$
A) $y ( x ) = e ^ { - 2 x } \left( c _ { 1 } + c _ { 2 } \frac { 1 } { 2 x } \right)$
B) $y ( x ) = e ^ { - 2 x } \left( c _ { 1 } + c _ { 2 } x + \frac { 1 } { 2 x } \right)$
C) $y ( x ) = e ^ { - 2 x } \left( c _ { 1 } + c _ { 2 } \right)$
D) $y ( x ) = e ^ { - 2 x } \left( c _ { 1 } + c _ { 2 } x \right) + \frac { 1 } { 2 x }$
E) $y ( x ) = e ^ { - 2 x } \left( c _ { 1 } + c _ { 2 } x + c _ { 3 } \frac { 1 } { 2 x } \right)$

Question

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The Answer is B

Solve the Differential Equation Using the Method of Variation of Parameters