Solve the Initial Value Problem $$\frac { d y } { d x } = \frac { 3 } { 1 + x ^ { 2 } } + \frac { 5 } { \sqrt { 1 - x ^ { 2 } } } , \quad y ( 0 ) = 6$$

question 4

Multiple Choice

Solve the initial value problem.
- $$\frac { d y } { d x } = \frac { 3 } { 1 + x ^ { 2 } } + \frac { 5 } { \sqrt { 1 - x ^ { 2 } } } , \quad y ( 0 ) = 6$$

• A) \(y = 3 \tan ^ { - 1 } x + 5 \sin ^ { - 1 } x + 6\)
• B) \(y = 3 \tan ^ { - 1 } x + 5 \sec ^ { - 1 } x + 3\)
• C) \(y = 3 \tan ^ { - 1 } x + 5 \sin ^ { - 1 } x + 3\)
• D) \(y = 3 \tan ^ { - 1 } x + 5 \sec ^ { - 1 } x + 6\)

---

Definitions:

Person-Centred Theory

A psychological approach emphasizing the importance of self-awareness and the innate tendency toward growth and fulfillment, developed by Carl Rogers.

Self-Actualization

Fulfilling one's abilities and potential, perceived as an inherent motivation or requirement in all individuals.

Individual Psychology

A psychological method or theory developed by Alfred Adler, focusing on the uniqueness of each individual and his or her holistic approach to life.

Phenomenological Approach

A research method focusing on individuals' subjective experiences and interpretations of the world around them.