Solve the Differential Equation $$y ^ {tt } - 8 y ^ { t } + 41 y = 0$$

question 102

Multiple Choice

Solve the differential equation. Select the correct answer.
$$y ^ {tt } - 8 y ^ { t } + 41 y = 0$$

• A) \(y ( x ) = e ^ { 4 x } \left( c _ { 1 } \cos ( 5 x ) + c _ { 2 } x \sin ( 5 x ) \right)\)
• B) \(y ( x ) = e ^ { 4 x } \left( c _ { 1 } \cos ( 5 x ) + c _ { 2 } \sin ( 5 x ) \right)\)
• C) \(y ( x ) = e ^ { 5 x } \left( c _ { 1 } \cos ( 4 x ) + c _ { 2 } \sin ( 4 x ) \right)\)
• D) \(y ( x ) = c e ^ { 4 x } \cos ( 5 x )\)
• E) \(y ( x ) = e ^ { 4 x } \left( c _ { 1 } \cos ( 4 x ) + c _ { 2 } x \sin ( 4 x ) \right)\)

Distinguish between explicit and implicit costs in decision-making.

Understand the reasons behind the purchase of insurance and its relation to risk aversion.

Identify the scenarios where individuals might make decisions that are not economically optimal due to irrational behaviors or misperceptions.

Understand the developmental stages of children's cognition and memory.

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