The Correct Form of the Particular Solution Of $y ^ { \prime \prime } - 2 y ^ { \prime } = x + e ^ { x }$

question 2

Multiple Choice

The correct form of the particular solution of $y ^ { \prime \prime } - 2 y ^ { \prime } = x + e ^ { x }$ is

• A) \(y _ { p } = A x + B + C e ^ { x }\)
• B) \(y _ { p } = \left( A x + B + C e ^ { x } \right) x\)
• C) \(y _ { p } = A x ^ { 2 } + B + C e ^ { x }\)
• D) \(y _ { p } = A x ^ { 2 } + B x + C e ^ { x }\)
• E) \(y _ { p } = A x + B + C x e ^ { x }\)

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Definitions:

Purely Competitive

A market scenario where products are identical, leading to numerous sellers and buyers where no single entity can influence market prices.

Marginal Cost

The cost of producing one additional unit of a product or service, crucial for decision-making about production levels and pricing.

Opportunity Cost

The cost of foregone alternatives when one choice is made over another, representing the benefits that could have been gained by choosing the next best alternative.

Purely Competitive

Refers to a market structure characterized by a large number of small firms, a homogeneous product, and very easy entry and exit.