Find a Trial Solution for the Method of Undetermined Coefficients $y ^ { \prime \prime } + 3 y ^ { \prime } + 5 y = x ^ { 4 } e ^ { 9 x }$

question 32

Multiple Choice

Find a trial solution for the method of undetermined coefficients. Do not determine the coefficients. $y ^ { \prime \prime } + 3 y ^ { \prime } + 5 y = x ^ { 4 } e ^ { 9 x }$

• A) \(y _ { y } ( x ) = \left( A x ^ { 4 } + B x ^ { 2 } + C \right) e ^ { - 9 x }\)
• B) \(y _ { y } ( x ) = \left( A x ^ { 3 } + B x ^ { 2 } + C x + D \right) e ^ { 9 x }\)
• C) \(y _ { y } ( x ) = \left( A x ^ { 4 } + B \right) e ^ { 9 x }\)
• D) \(y _ { y } ( x ) = A x ^ { 9 }\)
• E) \(y _ { y } ( x ) = \left( A x ^ { 4 } + B x ^ { 3 } + C x ^ { 2 } + D x + E \right) e ^ { 9 x }\)

---

Definitions:

Financial Aid

Monetary assistance provided to individuals, typically students, to help cover the cost of education or other expenses.

High-Performing Teams

Groups that exhibit a high level of collaboration and innovation, and consistently achieve superior results.

Unison

involves acting or speaking simultaneously or in agreement, exhibiting a unified or harmonious conformity.

Happenstance

An event or occurrence that happens by chance, without apparent cause.