The Solution of the Equation for the Differential Equation $x ^ { 2 } y ^ { \prime \prime } - 2 x y ^ { \prime } + 2 y = 0$

question 15

Multiple Choice

The solution of the equation for the differential equation $x ^ { 2 } y ^ { \prime \prime } - 2 x y ^ { \prime } + 2 y = 0$ is

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

---

Definitions:

Terrorist Mentality

A psychological framework that motivates individuals to engage in or support acts of terrorism, often driven by ideological, political, or religious convictions.

Group Interaction

The dynamics and processes that occur when individuals come together to form a group, influencing each other's behaviors and attitudes.

Deindividuation

A psychological state where an individual loses their self-awareness and sense of individuality, often leading to uncharacteristic behavior, usually as a result of being in a large group.

Self-Awareness

Acquaintance with one's own character aspects, feelings, aims, and desires.