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

question 1

True/False

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

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Definitions:

Spatial-Physical

Relates to the ability to understand and manipulate the physical world, including navigating space and manipulating objects.

Piaget's Cognitive Development

A theory by Jean Piaget that outlines how children's cognitive abilities develop through four stages from infancy to adolescence, emphasizing the construction of understanding through interactions with the environment.

Assimilation

The cognitive process of fitting new information into pre-existing cognitive schemas, perceptions, and understanding.

Accommodation

The process of adjusting or adapting cognitive frameworks or behaviors to better align with external realities or requirements.