Solve the Differential Equation $$x \frac { d y } { d x } + 2 y = 4 - \frac { 1 } { x } , x > 0$$

question 37

Multiple Choice

Solve the differential equation.
- $$x \frac { d y } { d x } + 2 y = 4 - \frac { 1 } { x } , x > 0$$

• A) \(y = \frac { 4 x ^ { 2 } - 2 x + C } { 2 x ^ { 2 } } , x > 0\)
• B) \(y = \frac { 4 x ^ { 2 } - x + C } { 2 x ^ { 2 } } , x > 0\)
• C) \(y = \frac { x ^ { 2 } - 4 x + C } { 2 x ^ { 2 } } , x > 0\)
• D) \(y = \frac { 4 x ^ { 2 } + 2 x + C } { 2 x ^ { 2 } } , x > 0\)

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Definitions:

Declarative Memory

Declarative memory refers to the recall of specific facts and events that can be consciously verbalized.

Corticobulbar

Pertaining to neural pathways that connect the cerebral cortex to the brainstem, involved in movement control.

Corticospinal

Pertaining to the motor pathways that travel from the cerebral cortex to the spinal cord, involved in voluntary movement control.

Direct Motor Pathways

Neural paths descending from the brain to the spinal cord responsible for the voluntary movement of muscles.