The Solution of the Differential Equation $x ^ { 2 } y ^ { \prime \prime } - 3 x y ^ { \prime } + 4 y = 0$

question 37

Multiple Choice

The solution of the differential equation $x ^ { 2 } y ^ { \prime \prime } - 3 x y ^ { \prime } + 4 y = 0$ is

• A) \(y = c _ { 1 } x + c _ { 2 } x ^ { 2 }\)
• B) \(y = c _ { 1 } x + c _ { 2 } x ^ { 3 }\)
• C) \(y = c _ { 1 } x ^ { ( 3 + \sqrt { 7 } ) / 2 } + c _ { 2 } x ^ { ( 3 - \sqrt { 7 } ) / 2 }\)
• D) \(y = c _ { 1 } x ^ { 2 } + c _ { 2 } x ^ { 2 } \ln x\)
• E) \(y = c _ { 1 } x + c _ { 2 } x \ln x\)

Understand the roles and types of questions in surveys and research.

Understand the importance of using a representative sample in surveys to ensure validity and reliability of data collected.

Identify the characteristics and limitations of closed and open-ended questions in data collection.

Distinguish between the reliability and validity of a survey and its impact on survey outcomes.

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Definitions:

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A natural resource that can replenish itself over time through natural processes, such as sunlight, wind, rain, tides, and geothermal heat, making it sustainable for ongoing use.

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The increase in extreme weather patterns linked to global warming.

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Powerful tropical storms with strong winds and heavy rain, known for their potential to cause significant damage.

Tornadoes

Violently rotating columns of air that are in contact with both the surface of the Earth and a cumulonimbus cloud or, in rare cases, the base of a cumulus cloud.