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

question 97

Multiple Choice

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

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

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Definitions:

Infant Crying

The vocal expression of distress or discomfort in infants, which can serve as a communication method to signal various needs.

Loud

Producing or capable of producing a high level of sound; not quiet.

Sudden

Occurring or done quickly and unexpectedly, without warning.

Emotional Regulation

The process of managing and responding to one's emotions in a healthy and productive manner.