Solve the Initial-Value Problem $$y ^ { tt} - 2 y ^ { t } - 24 y = 0 , y ( 1 ) = 4 , y ^ { t } ( 1 ) = 8$$

question 23

Multiple Choice

Solve the initial-value problem. Select the correct answer.
$$y ^ { tt} - 2 y ^ { t } - 24 y = 0 , y ( 1 ) = 4 , y ^ { t } ( 1 ) = 8$$

• A)
• \(y ( x ) = \frac { 1 } { 10 } e ^ { x } - \frac { 1 } { 23 } e ^ { - x }\)
• B)
• \(y ( x ) = \frac { 1 } { 10 } e ^ { 4 ( x - 1 ) } + \frac { 1 } { 23 } e ^ { - 6 ( x - 1 ) }\)
• C) \(y ( x ) = e ^ { 6 x } - e ^ { - 4 x }\)
• D)
• \(y ( x ) = \frac { 24 } { 10 } e ^ { 6 ( x - 1 ) } + \frac { 16 } { 10 } e ^ { - 4 ( x - 1 ) }\)
• E)
• \(y ( x ) = \frac { 1 } { 10 } e ^ { 4 x } - \frac { 1 } { 23 } e ^ { - 6 x }\)

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Definitions:

Visual Cortex

The part of the cerebral cortex responsible for processing visual information, located in the back of the brain.

Feature Detection

The process in which the brain identifies specific elements of visuals, such as lines, edges, or movements, to interpret what is seen.

Parallel Processing

The brain's ability to simultaneously process incoming stimuli of differing quality, a fundamental method our brains use to understand and interact with the world.

Parallel Processing

The ability of the brain to process multiple information streams simultaneously, enhancing efficiency in perception and thinking.