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:

Market Rate

The prevailing rate of interest or value for currencies or goods in the marketplace, often influenced by supply and demand.

Effective Interest Rate Method

A technique used in finance to find the actual interest rate per period with compounding taken into account.

Amortizing

The process of gradually paying off a debt over a period of time through regular payments.

Bond Discount

The difference between the bond's face value and its selling price when the bond is sold for less than its face value.