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

question 14

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

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