Solve the Differential Equation Using the Method of Undetermined Coefficients $y ^ { \prime \prime } + 6 y ^ { \prime } + 9 y = 2 + x$

question 29

Multiple Choice

Solve the differential equation using the method of undetermined coefficients. $y ^ { \prime \prime } + 6 y ^ { \prime } + 9 y = 2 + x$

• A) \(y ( x ) = c _ { 1 } e ^ { - 3 x } + c _ { 2 } x e ^ { - 3 x } + \frac { 2 } { 9 } x + \frac { 4 } { 27 }\)
• B) \(y ( x ) = c _ { 1 } e ^ { - 3 x } + c _ { 2 } x e ^ { - 3 x }\)
• C) \(y ( x ) = c _ { 1 } e ^ { - 3 x } + c _ { 2 } x e ^ { - 3 x } + \frac { 2 } { 9 } x\)
• D) \(y ( x ) = c _ { 1 } e ^ { - 3 x } + \frac { 2 } { 9 } x + \frac { 4 } { 27 }\)
• E) \(y ( x ) = c _ { 1 } x e ^ { - 3 x } + c _ { 2 } x ^ { 2 } e ^ { - 3 x } + \frac { 4 } { 27 } x\)

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