Solve the Differential Equation $\frac { d ^ { 2 } y } { d t ^ { 2 } } + \frac { d y } { d t } + 3 y = 0$

question 39

Multiple Choice

Solve the differential equation. $\frac { d ^ { 2 } y } { d t ^ { 2 } } + \frac { d y } { d t } + 3 y = 0$

• A) \(y ( t ) = t e ^ { \frac { t } { 2 } } \left[ c _ { 1 } \cos \left( \frac { \sqrt { 11 } t } { 2 } \right) + c _ { 2 } \sin \left( \frac { \sqrt { 11 } t } { 2 } \right) \right]\)
• B) \(y ( t ) = e ^ { \frac { \sqrt { 2 } } { 2 } } \left[ c _ { 1 } \cos \left( \frac { \sqrt { t } } { 2 } \right) + c _ { 2 } \sin \left( \frac { \sqrt { t } } { 2 } \right) \right]\)
• C) \(y ( t ) = e ^ { - \frac { t } { 2 } } \left[ c _ { 1 } \cos \left( \frac { \sqrt { 11 } t } { 2 } \right) + c _ { 2 } \sin \left( \frac { \sqrt { 11 } t } { 2 } \right) \right]\)
• D) \(y ( t ) = t ^ { 2 } e ^ { - \frac { t } { 2 } } \left[ c _ { 1 } \cos \left( \sqrt { \frac { 11 t } { 2 } } \right) + c _ { 2 } \sin \left( \sqrt { \frac { 11 t } { 2 } } \right) \right]\)
• E) \(y ( t ) = c e ^ { - \frac { t } { 2 } } \cos \left( \sqrt { \frac { 11 t } { 2 } } \right)\)

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