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) $y _ { y } ( x ) = \left( A x ^ { 4 } + B \right) e ^ { 5 x }$

Question

Quizplus · Accepted Answer

The trial solution should match the form of the non-homogeneous term $x^4 e^{5x}$. Since the polynomial is of degree 4, the trial solution should be a polynomial of the same degree multiplied by $e^{5x}$.

Find a Trial Solution for the Method of Undetermined Coefficients ytt+3yt+5y=x4e5xy ^ { tt } + 3 y ^ {t } + 5 y = x ^ { 4 } e ^ { 5 x }ytt+3yt+5y=x4e5x

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