Solve the Boundary-Value Problem, If Possible $y ^ { \prime \prime } + 5 y ^ { \prime } - 36 y = 0 , y ( 0 ) = 0 , y ( 2 ) = 1$

question 56

Multiple Choice

Solve the boundary-value problem, if possible. $y ^ { \prime \prime } + 5 y ^ { \prime } - 36 y = 0 , y ( 0 ) = 0 , y ( 2 ) = 1$

• A) \(y ( x ) = \left( e ^ { 8 } - e ^ { - 18 } \right) ^ { - 1 } \left( e ^ { 4 x } - e ^ { - 9 x } \right)\)
• B) \(y ( x ) = \left( e ^ { 4 } - e ^ { - 18 } \right) \left( e ^ { 4 x } - e ^ { - 9 x } \right)\)
• C) \(y ( x ) = \left( e ^ { 9 } - e ^ { - 18 } \right) ^ { - 1 } \left( e ^ { x } - e ^ { - 9 x } \right)\)
• D) \(y ( x ) = \left( e ^ { 4 } - e ^ { - 18 } \right) ^ { - 1 } \left( e ^ { 4 x } - e ^ { - 9 x } \right)\)
• E) No solution

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Definitions:

Right Choice

Making a decision or selection that is considered correct or most fitting based on circumstances or objectives.

Situational Ethics

An ethical theory that posits the morality of an action is determined by the context or situation, rather than by applying universal laws.

Immanuel Kant

An 18th-century German philosopher, known for his work in epistemology, ethics, and aesthetics, emphasizing duty, rationality, and the categorical imperative.

Ethical Fundamentalist

An individual who adheres strictly to a set of ethical rules or principles, often with a belief that these principles are universally applicable.