Solve the Differential Equation $y ^ { \prime \prime } - 8 y ^ { \prime } + 25 y = 0$

question 5

Multiple Choice

Solve the differential equation. $y ^ { \prime \prime } - 8 y ^ { \prime } + 25 y = 0$

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

---

Definitions:

Online Relationships

Social connections made between individuals through the internet, which can include friendships, romantic relationships, or other social interactions.

Similarity

A state or condition of being alike, sharing common traits or attributes among individuals, objects, or concepts.

Initial Attraction

The first phase of attraction between people, which can be influenced by various factors such as physical appearance, social status, and personality traits.

Self-Disclosure

The act of revealing personal, private, or sensitive information about oneself to others, which can build trust and intimacy in relationships.