Using Laplace Transform Methods, the Solution Of $y ^ { \prime \prime } + 2 y ^ { \prime } + y = e ^ { - t } , y ( 0 ) = 1 , y ^ { \prime } ( 0 ) = 0$

question 27

Multiple Choice

Using Laplace transform methods, the solution of $y ^ { \prime \prime } + 2 y ^ { \prime } + y = e ^ { - t } , y ( 0 ) = 1 , y ^ { \prime } ( 0 ) = 0$ is

• A) \(y = e ^ { t } + t e ^ { t } + t ^ { 2 } e ^ { t } / 2\)
• B) \(y = e ^ { - t } + t e ^ { - t } + t ^ { 2 } e ^ { - t } / 2\)
• C) \(y = e ^ { t } - t e ^ { t } + t ^ { 2 } e ^ { t } / 2\)
• D) \(y = e ^ { - t } - t e ^ { - t } - t ^ { 2 } e ^ { - t } / 2\)
• E) \(y = e ^ { - t } + t e ^ { - t } - t ^ { 2 } e ^ { - t } / 2\)

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