The Solution of the Initial Value Problem $y ^ { \prime } = 2 y + x , y ( - 1 ) = 1 / 2$

question 9

Multiple Choice

The solution of the initial value problem $y ^ { \prime } = 2 y + x , y ( - 1 ) = 1 / 2$ is $y = - x / 2 - 1 / 4 + c e ^ { 2 x }$ , where $c =$

• A) 2
• B) \(e ^ { 2 } / 4\)
• C) \(e ^ { 2 }\)
• D) \(e ^ { 2 } / 2\)
• E) 1

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Definitions:

Marginal Cost

The cost added by producing one additional unit of a product or service, a concept used in economics and financial management to analyze and make decisions.

Maximize Profits

The process by which a business seeks to achieve the highest possible return from its operations, often through optimizing costs, pricing, and production strategies.

Marginal Revenue

The additional revenue that an entity receives from selling one more unit of a good or service.

Average Revenue

The amount of revenue received per unit of a good or service sold, calculated by dividing total revenue by the total number of units sold.