Solve the Differential Equation $\frac { d u } { d t } = 15 + 5 u + 3 t + u t$

question 35

Multiple Choice

Solve the differential equation.
$\frac { d u } { d t } = 15 + 5 u + 3 t + u t$

• A)
• \(u = - 3 + C e ^ { \frac { t ^ { 2 } } { 2 } - 5 t }\)
• B)
• \(u = - 3 + C e ^ { t ^ { 2 } - 5 t }\)
• C)
• \(u = - 3 + C e ^ { \frac { t ^ { 2 } } { 2 } + 5 t }\)
• D)
• \(u = - 3 + C e ^ { \frac { t ^ { 2 } } { 2 } + 5 t ^ { 2 } }\)
• E) \(u = - 3 + C e ^ { t ^ { 2 } + 5 t }\)

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Definitions:

Degree of Operating Leverage

A measure of how much a company's operating income changes in response to a change in sales volume, indicating the level of fixed versus variable costs.

Contribution Margin

The amount remaining from sales revenue after all variable expenses have been deducted, indicating the ability to cover fixed costs and generate profit.

Total Contribution Margin

The difference between total sales revenue and total variable costs, measuring how much revenue covers fixed costs and profits.

CVP Graph

A visual representation of the Cost-Volume-Profit analysis that illustrates the relationships between costs, volume, and profit.