Solve the Differential Equation $y ^ {tt} - 6 y ^ { t } + 9 y = 8 x ^ { 2 } e ^ { 3 x } \text { by the method of variation of }$

question 21

Multiple Choice

Solve the differential equation $y ^ {tt} - 6 y ^ { t } + 9 y = 8 x ^ { 2 } e ^ { 3 x } \text { by the method of variation of }$ parameters.

• A) \(y = \left( C _ { 1 } + C _ { 2 } x + \frac { 2 } { 3 } x ^ { 4 } \right) e ^ { 3 x }\)
• B) \(y = \left( C _ { 1 } + C _ { 2 } x + \frac { 8 } { 15 } x ^ { 4 } \right) e ^ { 3 x }\)
• C)\(y = \left( C _ { 1 } + C _ { 2 } x + \frac { 4 } { 9 } x ^ { 2 } \right) e ^ { 3 x }\)
• D)\(y = \left( C _ { 1 } + C _ { 2 } x - \frac { 8 } { 17 } x ^ { 2 } \right) e ^ { 3 x }\)
• E)\(y = \left( C _ { 1 } + C _ { 2 } x - \frac { 4 } { 5 } x ^ { 2 } \right) e ^ { 3 x }\)

---

Definitions:

Ritualistic Hand Washing

A behavior often associated with obsessive-compulsive disorder, characterized by excessive and repetitive washing of hands in a ritualistic manner.

Effective Coping

The use of healthy strategies to deal with stress or adversity, maintain emotional well-being, and resolve conflicts.

Social Activities

Activities designed to facilitate interaction and communication among people, promoting social connections and a sense of community.

Severe Anxiety

An intense state of fear or dread that can interfere with daily activities, often requiring professional intervention for management.