Find the General Solution of the Linear Differential Equation $$y ^ { ttt} - 13 y ^ { tt } + 54 y ^ {t } - 72 y = 0 .$$

question 45

Multiple Choice

Find the general solution of the linear differential equation $$y ^ { ttt} - 13 y ^ { tt } + 54 y ^ {t } - 72 y = 0 .$$

• A) \(y = C _ { 1 } e ^ { 3 x } - 6 C _ { 2 } e ^ { - 6 x } + C _ { 3 } e ^ { 4 x }\)
• B) \(y = C _ { 1 } e ^ { 3 x } + C _ { 2 } e ^ { 6 x } + C _ { 3 } e ^ { 4 x }\)
• C) \(y = C _ { 1 } e ^ { - 3 x } + 6 C _ { 2 } e ^ { 6 x } + 4 C _ { 3 } e ^ { 4 x }\)
• D) \(y = C _ { 1 } e ^ { 3 x } - 6 C _ { 2 } e ^ { - 6 x } - 4 C _ { 3 } e ^ { - 4 x }\)
• E) \(y = C _ { 1 } e ^ { 3 x } + C _ { 2 } e ^ { 6 x } - 4 C _ { 3 } e ^ { - 4 x }\)

---

Definitions:

Foreign Individual

A person who comes from or resides in a different country than the one being referred to.

Third-Country Nationals

Individuals who are working in a country that is neither their home country nor the country of the business for which they are working.

Home Country

The country in which a multinational company is headquartered or where an individual originates from.

Guest Workers

Foreign workers invited to perform needed labour.