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

question 31

Multiple Choice

Without solving for the undetermined coefficients, the correct form of a particular solution of the differential equation $y ^ { \prime \prime } + 4 y ^ { \prime } + 5 y = e ^ { - 2 x } \cos x$ is

• A) \(y _ { p } = A e ^ { - 2 x } \cos x\)
• B) \(y _ { p } = A e ^ { - 2 x } \cos x + B e ^ { - 2 x } \sin x\)
• C) \(y _ { p } = A e ^ { - 2 x } \sin x\)
• D) \(y _ { p } = A x e ^ { - 2 x } \cos x + B x e ^ { - 2 x } \sin x\)
• E) \(y _ { p } = A x e ^ { - 2 x } \cos x + B e ^ { - 2 x } \sin x\)

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