Solve the Differential Equation Using the Method of Undetermined Coefficients $$y ^ { tt} - 3 y ^ { t } = \sin 9 x$$

question 20

Multiple Choice

Solve the differential equation using the method of undetermined coefficients. $$y ^ { tt} - 3 y ^ { t } = \sin 9 x$$

• A) \(y ( x ) = c _ { 1 } + c _ { 2 } e ^ { 3 x } - \frac { 1 } { 90 } \sin ( 6 x )\)
• B) \(y ( x ) = c _ { 1 } e ^ { 3 x } + \frac { 1 } { 90 } \cos ( 6 x ) + \frac { 1 } { 270 } \sin ( 6 x )\)
• C) \(y ( x ) = c _ { 1 } + c _ { 2 } e ^ { 3 x } + \frac { 1 } { 270 } \cos ( 6 x ) - \frac { 1 } { 90 } \sin ( 6 x )\)
• D) \(y ( x ) = c _ { 1 } e ^ { 3 x } + \frac { 1 } { 270 } \cos ( 6 x ) - \frac { 1 } { 90 } \sin ( 6 x )\)
• E) \(y ( x ) = \frac { 1 } { 270 } \cos ( 6 x ) - \frac { 1 } { 90 } \sin ( 6 x )\)

---

Definitions:

Rule Of Law

A principle that governs a society where laws are publicly promulgated, equally enforced, and independently adjudicated, and are consistent with international human rights principles.

Effective

Capable of producing intended or desired results, often used to describe techniques, policies, or actions that achieve their objectives efficiently.

Society

A group of individuals involved in persistent social interaction, or a large social grouping sharing the same geographical or virtual territory, subject to the same political authority and dominant cultural expectations.

Reciprocity

The obligation to return in kind what another has done for us.