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

question 57

Multiple Choice

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

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

---

Definitions:

Criminal Patterns

The recurring behaviors or methods that characterize criminal activity, often analyzed to predict or prevent future crimes.

Anticriminal Patterns

Behaviors or practices that are aimed at preventing crime or reducing the likelihood of engaging in criminal activity.

Conventional Society

A society that adheres to traditional norms and practices, often resisting change or innovation.

Attachment

A deep and enduring emotional bond that connects one person to another across time and space, often discussed in the context of child development.