A Particular Solution of the Differential Equation $y ^ { \prime \prime } + 2 y ^ { \prime } + y = e ^ { - x }$

question 32

Multiple Choice

A particular solution of the differential equation $y ^ { \prime \prime } + 2 y ^ { \prime } + y = e ^ { - x }$ is

• A) \(y _ { p } = x ^ { 2 } e ^ { - x } / 2\)
• B) \(y _ { p } = x e ^ { - x } / 2\)
• C) \(y _ { p } = x e ^ { - x }\)
• D) \(y _ { p } = e ^ { - x }\)
• E) \(y _ { p } = e ^ { - x } / 4\)

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