Solve the Initial-Value Problem $y ^ { \prime \prime } + 8 y ^ { \prime } + 41 y = 0 , y ( 0 ) = 1 , y ^ { \prime } ( 0 ) = 7$

question 44

Multiple Choice

Solve the initial-value problem. $y ^ { \prime \prime } + 8 y ^ { \prime } + 41 y = 0 , y ( 0 ) = 1 , y ^ { \prime } ( 0 ) = 7$

• A) \(y = e ^ { 5 x } \left( \cos ( 5 x ) + \frac { 11 } { 5 } \sin ( 5 x ) \right)\)
• B) \(y = e ^ { - 5 x } \left( \cos ( 5 x ) + \frac { 2 } { 5 } \sin ( 5 x ) \right)\)
• C) \(y = e ^ { 5 x } \left( \cos ( 4 x ) + \frac { 11 } { 5 } \sin ( 4 x ) \right)\)
• D) \(y = e ^ { - 4 x } \left( \cos ( 5 x ) + \frac { 11 } { 5 } \sin ( 5 x ) \right)\)
• E) \(y = e ^ { 4 x } \left( \cos ( 5 x ) - \frac { 2 } { 5 } \sin ( 5 x ) \right)\)

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Definitions:

Efficient Frontier

A concept in portfolio theory representing the set of optimal portfolios offering the maximum expected return for a given level of risk or the minimum risk for a certain level of expected return.

Degree-Of-Risk Tolerance

The level of variability in investment returns that an investor is willing to withstand in their investment portfolio.

Risk Aversion

The preference to avoid uncertainty in investment decisions, showing a tendency to prefer safer investments over riskier ones.

Capital Gains Tax

The tax on the profit made from the sale of a non-inventory asset when the sale price exceeds the purchase price.