The Solution Of $y ^ { \prime \prime } - 4 y ^ { \prime } + 13 y = 0$

question 14

Multiple Choice

The solution of $y ^ { \prime \prime } - 4 y ^ { \prime } + 13 y = 0$ is

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

---

Definitions:

Dreams

A sequence of thoughts, images, and sensations occurring in a person's mind during sleep.

NREM Sleep

A phase of sleep characterized by non-rapid eye movement, consisting of stages 1-3, each deeper than the last, and associated with physical and mental restoration.

REM Sleep

A unique phase of sleep characterized by rapid eye movements, low muscle tone, and vivid dreams, playing a key role in emotional regulation and memory.

Vivid Dreams

Highly detailed, clear, and sometimes intensely emotional dreams that are remembered upon awakening.