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

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Latent Learning

A form of learning that occurs without any obvious reinforcement of the behavior or associations that are learned, becoming apparent only when there is an incentive to demonstrate it.

Reinforced Behaviors

Actions that are encouraged and increased in frequency due to the application of a positive or negative stimulus following the behavior.

Internal Colonialism

Involves one race or ethnic group subjugating another in the same country. It prevents assimilation by segregating the subordinate group in terms of jobs, housing, and social contacts.

Expulsion

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