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

question 15

Multiple Choice

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

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

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Definitions:

If … Then Model

A cognitive-behavioral framework suggesting that individuals' reactions are conditional responses based on their personality and the specifics of the situation.

Watson's S-R Connection

Refers to John B. Watson's theory in behaviorism emphasizing the stimulus-response (S-R) connection, suggesting that behavior is a result of external stimuli.

Mischel

A psychologist known for his work on personality theory and cognitive-affective systems, suggesting that behavior is influenced more by situational factors than by innate traits.

Nomothetic Goals

Refers to the objectives or aims that can be applied universally, emphasizing general laws and traits that can be studied across individuals.