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:

Balance Sheet

A financial statement that shows the assets, liabilities, and shareholders' equity of a company at a specific point in time, providing a snapshot of its financial condition.

External Financing Needed

The additional funding required by a firm to finance its business activities and growth outside of internal cash flows.

Dividend Payout Ratio

The percentage of a company's earnings paid out to shareholders in the form of dividends.

Profit Margin Ratio

A financial metric that measures the percentage of profit a company produces from its total revenue.