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

Since the differential equation has a term of the form $x^4e^{5x}$, we need to assume a trial solution of the form $y_p(x)=(Ax^4+Bx^3+Cx^2+Dx+E)e^{5x}$.

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 $y ^ { tt} + 3 y ^ { t } + 5 y = x ^ { 4 } e ^ { 5 x }$