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:

Non-compensatory Rule

A decision rule in which an option is rejected if it fails to meet at least one important criterion, regardless of its merits on other criteria.

Clever Hans Effect

The phenomenon where a creature (notably a horse named Clever Hans) appears to be able to perform tasks requiring intelligence, but is actually responding to cues from humans.

Negative Correlation

An association between two elements in which the rise of one leads to the fall of the other.

Causation

The action of causing something, implying a relationship where one event is the result of the occurrence of another event.