Find a Trial Solution for the Method of Undetermined Coefficients $$y ^ { tt } + 3 y ^ {t } + 5 y = x ^ { 4 } e ^ { 5 x }$$

question 153

Multiple Choice

Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients.
$$y ^ { tt } + 3 y ^ {t } + 5 y = x ^ { 4 } e ^ { 5 x }$$

• A) \(y _ { y } ( x ) = \left( A x ^ { 4 } + B x ^ { 2 } + C \right) e ^ { - 5 x }\)
• B) \(y _ { y } ( x ) = \left( A x ^ { 4 } + B x ^ { 3 } + C x ^ { 2 } + D x + E \right) e ^ { 5 x }\)
• C) \(y _ { y } ( x ) = \left( A x ^ { 3 } + B x ^ { 2 } + C x + D \right) e ^ { 5 x }\)
• D) \(y _ { y } ( x ) = A x ^ { 5 }\)
• E) \(y _ { y } ( x ) = \left( A x ^ { 4 } + B \right) e ^ { 5 x }\)

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