Solve the Initial-Value Problem $( 1 + \cos x ) \frac { d y } { d x } = \left( 2 + e ^ { - y } \right) \sin x , y ( 0 ) = 0$

question 29

Multiple Choice

Solve the initial-value problem. $( 1 + \cos x ) \frac { d y } { d x } = \left( 2 + e ^ { - y } \right) \sin x , y ( 0 ) = 0$

• A) \(y = \ln ( 2 - \cos x ) ( 2 + \cos x )\)
• B) \(y = \frac { ( 7 - \cos x ) } { ( 2 + \cos x ) }\)
• C) \(y = \ln \frac { \cos x } { ( 2 + \cos x ) }\)
• D) \(y = \frac { \ln ( 2 + \cos x ) } { \ln ( 2 - \cos x ) }\)
• E) \(y = \ln ( 7 - \cos x ) - \ln ( 1 + \cos x )\)

---

Definitions:

Factorial Experiment

A factorial experiment is a type of experiment where two or more factors are varied simultaneously to observe their effect on the experimental outcome.

Balanced

Refers to a situation in which different groups or factors in a study or experiment are of equal or nearly equal size or importance.

Experimental Design

The process of planning an experiment to ensure it can test hypotheses effectively and produce valid and reliable results.

Interaction

In statistics, it refers to situations where the effect of one variable on an outcome is modified by another variable.