Solve the Boundary-Value Problem, If Possible $$y ^ { tt } + 5 y ^ { t } - 24 y = 0 , y ( 0 ) = 0 , y ( 2 ) = 1$$

question 113

Multiple Choice

Solve the boundary-value problem, if possible.
$$y ^ { tt } + 5 y ^ { t } - 24 y = 0 , y ( 0 ) = 0 , y ( 2 ) = 1$$

• A) \(y ( x ) = \left( e ^ { 6 } - e ^ { - 16 } \right) ^ { - 1 } \left( e ^ { 3 x } - e ^ { - 8 x } \right)\)
• B) \(y ( x ) = \left( e ^ { 8 } - e ^ { - 16 } \right) ^ { - 1 } \left( e ^ { x } - e ^ { - 8 x } \right)\)
• C) \(y ( x ) = \left( e ^ { 3 } - e ^ { - 16 } \right) \left( e ^ { 3 x } - e ^ { - 8 x } \right)\)
• D) \(y ( x ) = \left( e ^ { 3 } - e ^ { - 16 } \right) ^ { - 1 } \left( e ^ { 3 x } - e ^ { - 8 x } \right)\)
• E) No solution

---

Definitions:

Produced Abroad

Refers to goods or services that are created or performed outside the borders of the home country, often considered in the context of imports and exports.

Greater Prosperity

An increased state of wealth, success, or economic well-being.

Trade

The exchange of goods or services between individuals, businesses, or countries.

Lower Opportunity Cost

The advantage of choosing an option that has a relatively smaller loss of potential gain from other alternatives.