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) \(y = \ln ( 7 - \cos x ) - \ln ( 1 + \cos x )\)

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Definitions:

Rational Emotive Therapy

A psychotherapy procedure introduced by Ellis that examines the irrational reasoning causing emotional problems.

A-B-C Process

A model in cognitive behavioral therapy outlining the sequence of Antecedent, Behavior, and Consequence.

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