Solve the Differential Equation Using the Method of Variation of Parameters

question 15

Multiple Choice

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) \(y ( x ) = e ^ { - 2 x } \left( c _ { 1 } + c _ { 2 } x + c _ { 3 } \frac { 1 } { 2 x } \right)\)

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