Solve the Differential Equation $$\frac { d ^ { 2 } y } { d t ^ { 2 } } + \frac { d y } { d t } + 4 y = 0$$

question 105

Multiple Choice

Solve the differential equation. Select the correct answer.
$$\frac { d ^ { 2 } y } { d t ^ { 2 } } + \frac { d y } { d t } + 4 y = 0$$

• A)
• \[y ( t ) = t e ^ { \frac { t } { 2 } } \left[ c _ { 1 } \cos \left( \frac { \sqrt { 15 } t } { 2 } \right) + c _ { 2 } \sin \left( \frac { \sqrt { 15 } t } { 2 } \right) \right]\]
• B)
• \[y ( t ) = t ^ { 2 } e ^ { - \frac { t } { 2 } } \left[ c _ { 1 } \cos \left( \sqrt { \frac { 15 t } { 2 } } \right) + c _ { 2 } \sin \left( \sqrt { \frac { 15 t } { 2 } } \right) \right]\]
• C)
• \[y ( t ) = e ^ { \frac { \sqrt { t } } { 2 } } \left[ c _ { 1 } \cos \left( \frac { \sqrt { t } } { 2 } \right) + c _ { 2 } \sin \left( \frac { \sqrt { t } } { 2 } \right) \right]\]
• D)
• \[y ( t ) = c e ^ { - \frac { t } { 2 } } \cos \left( \sqrt { \frac { 15 t } { 2 } } \right)\]
• E)
• \[y ( t ) = e ^ { - \frac { t } { 2 } } \left[ c _ { 1 } \cos \left( \frac { \sqrt { 15 } t } { 2 } \right) + c _ { 2 } \sin \left( \frac { \sqrt { 15 } t } { 2 } \right) \right]\]

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