Solve the Initial-Value Problem $y ^ { tt } + 8 y ^ { t } + 41 y = 0 , y ( 0 ) = 1 , y ^ { t } ( 0 ) = 5$

question 42

Multiple Choice

Solve the initial-value problem. $y ^ { tt } + 8 y ^ { t } + 41 y = 0 , y ( 0 ) = 1 , y ^ { t } ( 0 ) = 5$

• A)
• \(y = e ^ { 5 x } \left( \cos ( 5 x ) + \frac { 9 } { 5 } \sin ( 5 x ) \right)\)
• B)
• \(y = e ^ { 4 x } \left( \cos ( 5 x ) - \frac { 2 } { 5 } \sin ( 5 x ) \right)\)
• C)
• \(y = e ^ { - 4 x } \left( \cos ( 5 x ) + \frac { 9 } { 5 } \sin ( 5 x ) \right)\)
• D)
• \(y = e ^ { - 5 x } \left( \cos ( 5 x ) + \frac { 2 } { 5 } \sin ( 5 x ) \right)\)
• E)
• \(y = e ^ { 5 x } \left( \cos ( 4 x ) + \frac { 9 } { 5 } \sin ( 4 x ) \right)\)

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Definitions:

High-low Method

A technique used in managerial accounting to estimate fixed and variable costs by analyzing the highest and lowest levels of activity and their associated costs.

Electrical Cost

The expense incurred from consuming electricity in operations, often considered a variable cost in manufacturing or service provision environments.

Fixed Component

The portion of a cost or expense that remains constant regardless of changes in the level of activity or production.

Least-squares Regression

A statistical method used to determine the best-fit line that minimizes the sum of the squared differences between observed values and the values predicted by the line.