Without Solving for the Undetermined Coefficients, the Correct Form of a Particular

question 29

Multiple Choice

Without solving for the undetermined coefficients, the correct form of a particular solution of the differential equation $y ^ { \prime \prime } + 9 y = \sin ( 3 x )$ is

• A) \(y _ { p } = A \cos ( 3 x )\)
• B) \(y _ { p } = A x \cos ( 3 x ) + B x \sin ( 3 x )\)
• C) \(y _ { p } = A \sin ( 3 x )\)
• D) \(y _ { p } = A x \cos ( 3 x ) + B \sin ( 3 x )\)
• E) \(y _ { p } = A \cos ( 3 x ) + B \sin ( 3 x )\)

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