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:

Critical Of Fathers

The tendency to analyze or judge paternal figures more harshly or meticulously, often in the context of their roles and responsibilities within the family.

Difficult Job

Employment that is challenging due to factors like complexity, high responsibility, or stressful working conditions.

Authority

The power or right to give orders, make decisions, and enforce obedience, often held by individuals or institutions in positions of control.

Raising Kids

The act of nurturing, educating, and supporting children as they grow.