Solve the Differential Equation $$\frac { d y } { d x } - \frac { y } { x } = ( \ln x ) ^ { 5 }$$

question 38

Multiple Choice

Solve the differential equation.
- $$\frac { d y } { d x } - \frac { y } { x } = ( \ln x ) ^ { 5 }$$

• A) \(y = \frac { 1 } { 6 } ( \ln x ) ^ { 6 } + C x\)
• B) \(y = x ( \ln x ) ^ { 6 } + C x\)
• C) \(y = \frac { 1 } { 6 } x ( \ln x ) ^ { 6 } + C x\)
• D) \(y = \frac { 1 } { 6 } x ^ { 6 } + C x\)

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Definitions:

Indifferent

A term used in economics and decision theory to describe a situation where an individual or consumer does not prefer one option over another.

Diminishing Marginal

The principle that the marginal benefit of using or consuming one more unit of a good or service decreases as its quantity increases.

Rate

The speed at which a certain event occurs, often expressed as a quantity over time.

Substitution

The act of replacing one thing with another, especially a similar item, in response to changes in market conditions or personal preferences.