Solve the Initial Value Problem $$\frac { d y } { d x } = e ^ { 4 x } \cos e ^ { 4 x } , y ( 0 ) = 0$$

question 173

Multiple Choice

Solve the initial value problem.
- $$\frac { d y } { d x } = e ^ { 4 x } \cos e ^ { 4 x } , y ( 0 ) = 0$$

• A) \(y = \frac { 1 } { 4 } \sin x\)
• B) \(y = \frac { 1 } { 4 } \sin \mathrm { e } ^ { 4 x } - \frac { 1 } { 4 } \sin 1\)
• C) \(y = - \frac { 1 } { 4 } \sin e ^ { 4 x } + \frac { 1 } { 4 } \sin 1\)
• D) \(y = \frac { 1 } { 4 } \sin \mathrm { e } ^ { 4 \mathrm { x } } - \frac { 1 } { 4 }\)

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Definitions:

Classical Conditioning

A psychological process through which associations between a previously neutral stimulus and a naturally occurring stimulus are learned, leading to a learned response.

Premack Principle

A principle of reinforcement which states that a more probable behavior can reinforce a less probable behavior.

Law of Effect

A psychological principle stating that behaviors followed by satisfying consequences tend to be repeated, while those followed by unpleasant consequences are less likely to be repeated.

Cognitive Model

A theoretical approach that explains psychological phenomena by emphasizing mental processes, including perception, memory, and thought.