Solve the Differential Equation $$x \frac { d y } { d x } = \frac { \cos x } { x ^ { 2 } } - 3 y , x > 0$$

question 54

Multiple Choice

Solve the differential equation.
- $$x \frac { d y } { d x } = \frac { \cos x } { x ^ { 2 } } - 3 y , x > 0$$

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

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Definitions:

Citric Acid Cycle

A series of chemical reactions used by all aerobic organisms to generate energy through the oxidation of acetate derived from carbohydrates, fats, and proteins into carbon dioxide.

Glucose

serves as a primary source of energy in most organisms, critical for cellular respiration and metabolic processes.

Turn

In a molecular context, a turn refers to a type of secondary structure in proteins where the chain makes a sharp change in direction.

Glycolysis

The metabolic pathway that converts glucose into pyruvate, producing ATP and NADH in the process, functioning in the cytoplasm of the cell.