Find the First Eight Terms of the Power Series Representing $y ^ { tt } + 11 x ^ { 2 } y = 0$

question 16

Multiple Choice

Find the first eight terms of the power series representing independent solutions of the differential equation $y ^ { tt } + 11 x ^ { 2 } y = 0$ .

• A) \(y = a _ { 0 } \left( 1 - \frac { x ^ { 4 } } { 4 ! } + \frac { x ^ { 8 } } { 8 ! } - \frac { x ^ { 12 } } { 12 ! } + \cdots \right) + a _ { 1 } \left( \frac { x } { 1 ! } - \frac { x ^ { 5 } } { 5 ! } + \frac { x ^ { 9 } } { 9 ! } - \frac { x ^ { 13 } } { 13 ! } + \cdots \right)\), where \(a _ { 0 }\) and \(a _ { 1 }\) are arbitrary constants
• B)\(\begin{aligned}
• y = & a _ { 0 } \left( 1 - \frac { 11 \cdot x ^ { 4 } } { 4 \cdot 3 } + \frac { 11 ^ { 2 } \cdot x ^ { 8 } } { 8 \cdot 7 \cdot 4 \cdot 3 } - \frac { 11 ^ { 3 } \cdot x ^ { 12 } } { 12 \cdot 11 \cdot 8 \cdot 7 \cdot 4 \cdot 3 } + \cdots \right) \\
• & + a _ { 1 } \left( x - \frac { 11 \cdot x ^ { 5 } } { 5 \cdot 4 } + \frac { 11 ^ { 2 } \cdot x ^ { 7 } } { 9 \cdot 8 \cdot 5 \cdot 4 } - \frac { 11 ^ { 3 } \cdot x ^ { 9 } } { 13 \cdot 12 \cdot 9 \cdot 8 \cdot 5 \cdot 4 } + \cdots \right)
• \end{aligned}\)
• where \(a _ { 0 }\) and \(a _ { 1 }\) are arbitrary constants
• C) \(y = a _ { 0 } \left( 1 - \frac { 11 \cdot x ^ { 4 } } { 2 ! } + \frac { 11 ^ { 2 } \cdot x ^ { 8 } } { 6 ! } - \frac { 11 ^ { 3 } \cdot x ^ { 12 } } { 10 ! } + \cdots \right) + a _ { 1 } \left( \frac { x } { 1 ! } - \frac { 11 \cdot x ^ { 5 } } { 5 ! } + \frac { 11 ^ { 2 } \cdot x ^ { 9 } } { 7 ! } - \frac { 11 ^ { 3 } \cdot x ^ { 13 } } { 11 ! } + \cdots \right)\), where \(a _ { 0 }\) and \(a _ { 1 }\) are arbitrary constants
• D) \(y = a _ { 0 } \left( 1 - \frac { x ^ { 2 } } { 2 ! } - \frac { x ^ { 6 } } { 6 ! } - \frac { x ^ { 10 } } { 10 ! } + \cdots \right) + a _ { 1 } \left( \frac { x } { 1 ! } - \frac { x ^ { 3 } } { 3 ! } - \frac { x ^ { 7 } } { 7 ! } - \frac { x ^ { 11 } } { 11 ! } + \cdots \right)\), where \(a _ { 0 }\) and \(a _ { 1 }\) are arbitrary constants
• E)
• \(y = a _ { 0 } \left( 1 - \frac { 11 \cdot x ^ { 4 } } { 4 \cdot 3 } - \frac { 11 ^ { 2 } \cdot x ^ { 8 } } { 8 \cdot 7 } - \frac { 11 ^ { 3 } \cdot x ^ { 12 } } { 12 \cdot 11 } + \cdots \right) + a _ { 1 } \left( x - \frac { 11 \cdot x ^ { 5 } } { 5 \cdot 4 } - \frac { 11 ^ { 2 } \cdot x ^ { 9 } } { 9 \cdot 8 } - \frac { 11 ^ { 3 } \cdot x ^ { 13 } } { 13 \cdot 12 } + \cdots \right)\) where \(a _ { 0 }\) and \(a _ { 1 }\) are arbitrary constants

Analyze the debate between monism and dualism in the context of existence and reality.

Distinguish between empirical and rationalist approaches in the philosophical understanding of the world.

Identify philosophical arguments regarding the relationship between science, religion, and reality.

Grasp the significance of idealism and realism in the philosophy of science and knowledge.

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Employee benefit programs that allow individuals to choose from a variety of pre-tax benefits according to their personal needs and situations.

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A compensation system that bases employee pay on the skills, knowledge, and abilities they possess, rather than job title or position alone.

Skill-Based Pay

Skill-based pay is a compensation system where employees are paid based on the range, depth, and types of skills and knowledge they possess, rather than their job title or position.

Flexibility

The quality of being adaptable or variable, especially the ability to respond to changes in circumstances or environments.