Solve the Differential Equation Using the Method of Undetermined Coefficients $y ^ { \prime \prime } + 5 y ^ { \prime } + 6 y = x ^ { 2 }$

question 59

Multiple Choice

Solve the differential equation using the method of undetermined coefficients. $y ^ { \prime \prime } + 5 y ^ { \prime } + 6 y = x ^ { 2 }$

• A) \(y ( x ) = c _ { 1 } e ^ { - 2 x } + c _ { 2 } e ^ { - 3 x }\)
• B) \(y ( x ) = \frac { 1 } { 6 } x ^ { 2 } - \frac { 5 } { 18 } x + \frac { 19 } { 108 }\)
• C) \(y ( x ) = c _ { 1 } e ^ { - 2 x } + c _ { 2 } e ^ { - 3 x } + \frac { 1 } { 6 } x ^ { 2 }\)
• D) \(y ( x ) = c _ { 1 } e ^ { - 2 x } + c _ { 2 } e ^ { - 3 x } + \frac { 1 } { 6 } x ^ { 2 } - \frac { 5 } { 18 } x + \frac { 19 } { 108 }\)
• E) \(y ( x ) = c _ { 1 } e ^ { - 2 x } + c _ { 2 } e ^ { - 3 x } + \frac { 9 } { 108 } c _ { 3 }\)

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