$\text { Use integration to find a general solution of the differential equation } \frac { d y } { d x } = \frac { 3 x } { 3 + x ^ { 2 } } \text {. }$

question 37

Multiple Choice

$\text { Use integration to find a general solution of the differential equation } \frac { d y } { d x } = \frac { 3 x } { 3 + x ^ { 2 } } \text {. }$

• A) \(y = \frac { 3 } { 2 } \ln \left( \left| 3 + x ^ { 2 } \right| \right) + C\)
• B) \(y = \frac { 3 } { 2 x } \ln \left( \left| 6 + x ^ { 2 } \right| \right) + C\)
• C) \(y = \frac { 6 } { x ^ { 2 } } \ln \left( \left| 3 + x ^ { 2 } \right| \right) + C\)
• D) \(y = \frac { 3 } { x \ln \left( \left| 3 + x ^ { 2 } \right| \right) } + C\)
• E)\(y = \frac { 3 x ^ { 2 } } { \ln \left( \left| 3 + x ^ { 2 } \right| \right) } + C\)

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Definitions:

Output Levels

The quantity of goods or services produced by a company, sector, or economy in a given period of time.

Long Run

A period in economics where all factors of production and costs are variable, allowing full adjustment to any change in economic conditions.

Economies of Scale

The cost advantages that enterprises obtain due to their scale of operation, leading to a reduced cost per unit of output.

Average Variable Cost Curve

A graphical representation that shows how the average variable cost of production varies with the level of output.