Find the Solution to the Differential Equation $x y ^ { \prime } - ( 6 + x ) y = 0$

question 106

Multiple Choice

Find the solution to the differential equation $x y ^ { \prime } - ( 6 + x ) y = 0$ with $y ( 1 ) = 1$ , $y ( x ) \geq 0$ for all x.

• A) \(y = x ^ { 7 } e ^ { x }\)
• B) \(y = x ^ { 7 } e ^ { x - 1 }\)
• C) \(y = x ^ { 6 } e ^ { x - 1 }\)
• D) \(y = x ^ { 6 } e ^ { x } + 1 - e\)

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Definitions:

Behavioral Economics

A branch of economics that examines how psychological, emotional, cognitive, cultural, and social influences impact the economic choices made by individuals and institutions.

Economic Behavior

The study of how individuals, businesses, and governments make choices on allocating resources to satisfy their wants and needs.

Narrowly Self-Interested

Acting with only one's immediate personal benefit in mind, often disregarding the well-being or interests of others.

Behavioral Economists

Researchers who study the effects of psychological, cognitive, and emotional factors on economic decision-making.