Determine If the Given Function Y = F(x) Is a Solution

question 100

True/False

Determine if the given function y = f(x) is a solution of the accompanying differential equation.
-Differential equation: $2 xy ^ { \prime } + 2 y = \cos x$ Initial condition: $\mathrm { y } ( \pi ) = 0$
Solution candidate: $y = \frac { \sin x } { 2 x }$

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Definitions:

Expectancy

In psychology, the anticipation or belief regarding the likelihood that a particular behavior will lead to a specific outcome, heavily influencing motivations and actions.

Types of Expectancies

Different forms of anticipation or belief about what may happen in the future, often based on past experiences or social cues.

Stimulus Generalization

A conditioned response or operant behavior to a stimulus that is similar to the conditioned stimulus or discriminative stimulus.

Discriminative Operant

An operant behavior that is under the control of a discriminative stimulus