Use Power Series to Solve the Differential Equation $$y ^ { tt } + x ^ { 2 } y = 0 , y ( 0 ) = 6 , y ^ {t } ( 0 ) = 0$$

question 29

Multiple Choice

Use power series to solve the differential equation. $$y ^ { tt } + x ^ { 2 } y = 0 , y ( 0 ) = 6 , y ^ {t } ( 0 ) = 0$$

• A)\(y ( x ) = 6 - \sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { x ^ { 4 n } } { 4 n ( 4 n - 1 ) \cdot ( 4 n - 4 ) ( 4 n - 5 ) \cdots 4 \cdot 3 }\)
• B)\(y ( x ) = \sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { 6 x ^ { 4 n } } { 4 n ( 4 n - 1 ) \cdot ( 4 n - 4 ) ( 4 n - 5 ) \cdots 4 \cdot 3 }\)
• C)\(y ( x ) = 6 + \sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { 6 x ^ { 4 n } } { 4 n ( 4 n - 1 ) \cdot ( 4 n - 4 ) ( 4 n - 5 ) \cdots 4 \cdot 3 }\)
• D)\(y ( x ) = - 6 + \sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { x ^ { 4 n } } { 4 n ( 4 n - 1 ) \cdot ( 4 n - 4 ) ( 4 n - 5 ) \cdots 4 \cdot 3 }\)
• E)\(y ( x ) = \sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { x ^ { 4 n } } { 4 n ( 4 n - 1 ) \cdot ( 4 n - 4 ) ( 4 n - 5 ) \cdots 4 \cdot 3 }\)

---

Definitions:

Leadership Beliefs

The core principles or assumptions held by an individual about leadership, which can influence their approach and effectiveness as a leader.

Whistleblower

An individual who exposes illegal, unethical, or improper practices within an organization, often risking their own career or wellbeing for the sake of accountability and integrity.

Financial Misconduct

Unethical or illegal actions relating to financial dealings, such as embezzlement or fraud.

Unethical Behaviour

Actions or practices that violate social norms or standards, including honesty, integrity, and fairness.