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

question 28

Multiple Choice

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

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

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Definitions:

Field Devices

Field devices refer to any electronic equipment or sensors located in the "field," or operational environment, that gather data or interact with physical processes.

On Instruction

A programming command used to activate or turn on a specific process, function, or device within a control system.

ONS

In PLC programming, ONS (One Shot) refers to an instruction that allows a specific operation to execute only once for each activation of its input condition.

Program Scan

The sequential process by which a programmable logic controller (PLC) checks its inputs, executes its programmed logic, and updates its outputs.