Solve the Differential Equation $$x \frac { d y } { d x } = \frac { \cos x } { x ^ { 5 } } - 6 y , x > 0$$

question 68

Multiple Choice

Solve the differential equation.
- $$x \frac { d y } { d x } = \frac { \cos x } { x ^ { 5 } } - 6 y , x > 0$$

• A) \(y = x ^ { - 6 } ( \cos x + C ) , x > 0\)
• B) \(y = x ^ { 6 } ( \sin x + C ) , x > 0\)
• C) \(y = x ^ { 6 } ( \cos x + C ) , x > 0\)
• D) \(y = x ^ { - 6 } ( \sin x + C ) , x > 0\)

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Definitions:

Nasal Congestion

The blockage of nasal passages usually due to membranes lining the nose becoming swollen from inflamed blood vessels, often a symptom of a cold, allergy, or flu.

Runny Nose

The excessive discharge of mucus from the nasal passages, often a symptom of colds, allergies, or other irritations.

Incubation

The period between exposure to an infection and the appearance of the first symptoms.

Prodrome

An early symptom or set of symptoms that might indicate the start of a disease before specific symptoms occur.