Solve the Initial-Value Problem $( 1 + \cos x ) \frac { d y } { d x } = \left( 6 + e ^ { - y } \right) \sin x , y ( 0 ) = 0$

question 34

Multiple Choice

Solve the initial-value problem.
$( 1 + \cos x ) \frac { d y } { d x } = \left( 6 + e ^ { - y } \right) \sin x , y ( 0 ) = 0$

• A) \(y = \frac { \ln ( 6 + \cos x ) } { \ln ( 6 - \cos x ) }\)
• B)
• \(y = \ln \left( \frac { 1 } { 6 } \left( \sec ^ { 12 } \left( \frac { x } { 2 } \right) - 1 \right) \right.\)
• C) \(y = \ln ( 6 - \cos x ) ( 6 + \cos x )\)
• D)
• \(y = \ln \left( \frac { 1 } { 6 } \left( 7 \sec ^ { 12 } \left( \frac { x } { 2 } \right) - 1 \right) \right.\)
• E)
• \(y = \ln \left( 6 \sec \left( \frac { x } { 2 } \right) - 1 \right)\)

---

Definitions:

Communication Tool

Any device, platform, or method used to transmit information from one entity to another.

Nonprofits

Organizations that operate for charitable, educational, cultural, or social welfare purposes and do not distribute profits to owners or shareholders.

Economical

Characterized by efficiency and avoidance of waste, typically in terms of spending or resource utilization.

Social Media Profiles

The personal or business pages on social media platforms where users share their personal information, interests, and updates.