Solve the Initial-Value Problem $$y ^ { tt } - 2 y ^ { t } - 24 y = 0 , y ( 1 ) = 4 , y ^ { t } ( 1 ) = 6$$

question 35

Multiple Choice

Solve the initial-value problem. $$y ^ { tt } - 2 y ^ { t } - 24 y = 0 , y ( 1 ) = 4 , y ^ { t } ( 1 ) = 6$$

• A)\(y ( x ) = \frac { 22 } { 10 } e ^ { 6 ( x - 1 ) } + \frac { 18 } { 10 } e ^ { - 4 ( x - 1 ) }\)
• B) \(y ( x ) = e ^ { 6 x } - e ^ { - 4 x }\)
• C) \(y ( x ) = \frac { 1 } { 10 } e ^ { 4 ( x - 1 ) } + \frac { 1 } { 23 } e ^ { - 6 ( x - 1 ) }\)
• D) \(y ( x ) = \frac { 1 } { 10 } e ^ { x } - \frac { 1 } { 23 } e ^ { - x }\)
• E) \(y ( x ) = \frac { 1 } { 10 } e ^ { 4 x } - \frac { 1 } { 23 } e ^ { - 6 x }\)

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Definitions:

Episodic Memory

An enduring memory category focused on recalling distinct occurrences, contexts, and life experiences.

Mnemonic Device

Techniques a person can use to help them improve their ability to remember something.

Brain Waves

Patterns of electrical activity in the brain, measurable by EEG, which are indicators of different states of consciousness, such as sleep, relaxation, and focus.

Method of Loci

A mnemonic device that involves visualizing a familiar route or place to remember information sequentially by associating it with specific locations.