The Solution Of $x ^ { 2 } y ^ { \prime \prime } + 3 x y ^ { \prime } - 3 y = 0$

question 21

Multiple Choice

The solution of $x ^ { 2 } y ^ { \prime \prime } + 3 x y ^ { \prime } - 3 y = 0$ is

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

---

Definitions:

Cross-Sectional Study

A research method that involves observing a defined population at a single point in time or over a short period, making it possible to examine correlations and infer potential causations.

Cohort Differences

Variations in characteristics, experiences, or developments among groups of people who were born around the same time and share similar cultural or historical contexts.

Developmental Periods

Distinct phases of growth and change that an individual goes through during their lifespan, encompassing physical, cognitive, and emotional development.