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

Multiple Choice

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

A) $y _ { y _ { 1 } } ( x ) = A$
$y _ { y _ { 2 } } ( x ) = B x e ^ { 4 x }$

B) $y _ { y 1 } ( x ) = A x$
$y _ { y 2 } ( x ) = x ( A x + B ) e ^ { - 4 x }$

C) $y _ { y 1 } ( x ) = A$
$y _ { y _ { 2 } } ( x ) = x ( A + B ) e ^ { - 4 x }$

D) $y _ { p 11 } ( x ) = A x$
$y _ { p 22 } ( x ) = x ^ { 2 } ( A x + B ) e ^ { - 4 x }$

E) $y _ { y _ { 1 } } ( x ) = A$
$y _ { y 2 } ( x ) = x ( A + B x ) e ^ { - 4 x }$