Solve the Differential Equation $$y ^ { tt } - 8 y ^ { t } + 25 y = 0$$

question 68

Multiple Choice

Solve the differential equation. Select the correct answer.
$$y ^ { tt } - 8 y ^ { t } + 25 y = 0$$

• A) \(y = c e ^ { 4 x } \cos ( 3 x )\)
• B) \(y = c _ { 1 } \cos ( 3 x ) + c _ { 2 } x \sin ( 3 x )\)
• C) \(y = e ^ { 4 x } \left( c _ { 1 } \cos ( 3 x ) + c _ { 2 } \sin ( 3 x ) \right)\)
• D) \(y = e ^ { 4 x } \left( c _ { 1 } \cos ( 3 x ) + c _ { 2 } x \sin ( 3 x ) \right)\)
• E) \(y = e ^ { 4 x } \left( c _ { 1 } \cos ( 4 x ) + c _ { 2 } x \sin ( 4 x ) \right)\)

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Definitions:

FR-2 Schedule

A fixed-ratio schedule where reinforcement is provided after every second correct response.

FR-4 Schedule

A fixed-ratio schedule where a response is reinforced only after four instances of that response.

Prefrontal Cortex

The front part of the frontal lobes of the brain, involved in complex behaviors, decision making, and moderating social behavior.

Parietal Lobe

A region of the cerebral cortex that plays a key role in processing sensory information from various parts of the body, understanding spatial orientation, and navigation.