Solve the Differential Equation $$( 6 + t ) \frac { d u } { d t } + u = 6 + t , t > 0$$

question 154

Multiple Choice

Solve the differential equation. Select the correct answer.
$$( 6 + t ) \frac { d u } { d t } + u = 6 + t , t > 0$$

• A)
• \(u = \frac { t ^ { 2 } + C } { t + 6 }\)
• B)
• \(u = 6 t + \frac { t ^ { 2 } } { 6 } + C\)
• C)
• \[u = \frac { 6 t + t ^ { 2 } + C } { t + 6 }\]
• D)
• \[u = \frac { 6 t + \frac { t ^ { 2 } } { 2 } + C } { t + 6 }\]
• E)
• \[u = \frac { 6 t + \frac { 1 } { 2 } t ^ { 2 } } { \frac { 3 } { 6 } t + 2 } + C\]

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Definitions:

Conversion Costs

The combined costs of direct labor and manufacturing overheads that are incurred in transforming materials into finished goods.

Weighted-Average Method

A costing method that calculates the cost of goods sold and ending inventory based on the average cost of all units available for sale during a period.

Process Costing

A costing method used in production where costs are assigned to processes and then averaged over all units produced.

Job-Order Costing

An accounting method that assigns costs to specific jobs or batches, used in industries where goods or services are produced on a custom basis.