Solve the Differential Equation $$x y ^ { \prime } + 4 y = \frac { \cos x } { x ^ { 3 } } , x > 0$$

question 8

Multiple Choice

Solve the differential equation.
- $$x y ^ { \prime } + 4 y = \frac { \cos x } { x ^ { 3 } } , x > 0$$

• A) \(y = \frac { \cos x + C } { x ^ { 4 } } , x > 0\)
• B) \(y = \frac { \sin x + C } { x ^ { 3 } } , x > 0\)
• C) \(y = \frac { \sin x + C } { x ^ { 4 } } , x > 0\)
• D) \(y = \frac { \cos x + C } { x ^ { 3 } } , x > 0\)

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Definitions:

Max Weber

A foundational figure in sociology, known for his analysis of the relationship between the Protestant ethic and the spirit of capitalism, and for his theories on bureaucracy.

Socialists

Socialists are individuals or groups advocating for a political and economic system where the means of production, distribution, and exchange are owned or regulated by the community as a whole.

Bureaucracy

A system of management and administration characterized by hierarchical structure, defined roles and responsibilities, and a set of formal rules and procedures.

Rational Place

Refers to an environment or context in which decisions are made based on logical reasoning and empirical evidence.