Find a Trial Solution for the Method of Undetermined Coefficients $y ^ { \prime \prime } + 2 y ^ { \prime } = 1 + x e ^ { - 4 x }$

question 34

Multiple Choice

Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients. $y ^ { \prime \prime } + 2 y ^ { \prime } = 1 + x e ^ { - 4 x }$

• A) \(\begin{array} { l }
• y _ { p 1 } ( x ) = A \\
• y _ { p 2 } ( x ) = B x e ^ { 4 x }
• \end{array}\)
• B) \(\begin{array} { l }
• y _ { p 1 } ( x ) = A x \\
• y _ { p 2 } ( x ) = x ( A x + B ) e ^ { - 4 x }
• \end{array}\)
• C) \(\begin{array} { l }
• y _ { 71 } ( x ) = A \\
• y _ { p 2 } ( x ) = x ( A + B ) e ^ { - 4 x }
• \end{array}\)
• D) \(\begin{array} { l }
• y _ { p 1 } ( x ) = A x \\
• y _ { p 2 } ( x ) = x ^ { 2 } ( A x + B ) e ^ { - 4 x }
• \end{array}\)
• E) \(\begin{array} { l }
• y _ { p 1 } ( x ) = A \\
• y _ { p 2 } ( x ) = x ( A + B x ) e ^ { - 4 x }
• \end{array}\)

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