Solve the Differential Equation $$10 y ^ { tt } - x y ^ { t } - y = 0$$

question 1

Multiple Choice

Solve the differential equation $$10 y ^ { tt } - x y ^ { t } - y = 0$$

• A) \(y = a _ { 0 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n } } { 10 ^ { n } 2 ^ { n } n ! }\), where \(a _ { 0 }\) is an arbitrary constant
• B) \(y = a _ { 0 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n } } { 10 ^ { n } n ! } + a _ { 1 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n + 1 } } { ( n + 1 ) ! }\), where \(a _ { 0 }\) and \(a _ { 1 }\) are arbitrary constants
• C) \(y = a _ { 0 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n } } { 10 ^ { n } 2 ^ { n } n ! } + a _ { 1 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n + 1 } } { 10 ^ { n } \cdot 1 \cdot 3 \cdot 5 \cdot 7 \cdots ( 2 n + 1 ) }\), where \(a _ { 0 }\) and \(a _ { 1 }\) are arbitrary constants
• D) \(y = a _ { 0 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n } } { 10 ^ { n } 2 ^ { n + 1 } n ! } + a _ { 1 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n + 1 } } { 1 \cdot 3 \cdot 5 \cdot 7 \cdots ( 2 n + 1 ) }\), where \(a _ { 0 }\) and \(a _ { 1 }\) are arbitrary constants
• E) \(y = a _ { 0 } + a _ { 1 } \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n } } { 10 ^ { n } \cdot 1 \cdot 3 \cdot 5 \cdot 7 \cdots ( 2 n + 1 ) }\), where \(a _ { 0 }\) and \(a _ { 1 }\) are arbitrary constants

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Definitions:

Extinction

In psychology, the process by which a conditioned response diminishes and disappears following repeated exposure without reinforcement.

Stimulus Generalization

The process by which a conditioned response is triggered by stimuli that are similar, but not identical, to the original conditioned stimulus.

Superstitious Responding

A behavioral phenomenon where an individual develops a belief or practice around cause and effect relationships that are not logically connected.

Spontaneous Recovery

Spontaneous recovery is a term in psychology referring to the reappearance of a previously extinguished conditioned response after a pause.