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

question 30

Multiple Choice

Without solving for the undetermined coefficients, the correct form of a particular solution of the differential equation $y ^ { \prime \prime } + 6 y ^ { \prime } + 13 y = e ^ { - 3 x } \cos ( 2 x )$ is

• A) \(y _ { p } = A e ^ { - 3 x } \cos ( 2 x )\)
• B) \(y _ { p } = A e ^ { - 3 x } \cos ( 2 x ) + B e ^ { - 3 x } \sin ( 2 x )\)
• C) \(y _ { p } = A e ^ { 3 x } \cos ( 2 x )\)
• D) \(y _ {p } = A x e ^ { - 3 x } \cos ( 2 x ) + B x e ^ { - 3 x } \sin ( 2 x )\)
• E) \(y _ { p } = A x e ^ { - 3 x } \cos ( 2 x ) + B e ^ { - 3 x } \sin ( 2 x )\)