Solve the Differential Equation $$y ^ { tt } - 4 y ^ { t } + 20 y = 0$$

question 111

Multiple Choice

Solve the differential equation.
$$y ^ { tt } - 4 y ^ { t } + 20 y = 0$$

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