Solve the Differential Equation $$y ^ {tt } - 8 y ^ { t } + 32 y = 0$$

question 8

Multiple Choice

Solve the differential equation. $$y ^ {tt } - 8 y ^ { t } + 32 y = 0$$

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

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