An Integrating Factor for the Linear Differential Equation $y ^ { \prime } + y / x = x$

question 5

Multiple Choice

An integrating factor for the linear differential equation $y ^ { \prime } + y / x = x$ is

• A) \(1 / x\)
• B) \(x\)
• C) \(1 / x ^ { 2 }\)
• D) \(x ^ { 2 }\)
• E) \(e ^ { - x }\)

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Definitions:

Profit-Maximizing Output

The level of production that maximizes a firm’s profits, determined by the intersection of marginal cost and marginal revenue.

Total Revenue

The total income earned by a firm from selling its products or services, calculated as the quantity sold multiplied by the selling price.

Marginal Revenue

The additional income earned by selling one more unit of a product or service.

Minimum AVC

The lowest point on the Average Variable Cost curve, indicating the most efficient scale of production where variable costs per unit are minimized.