Find the Solution of the Initial-Value Problem $y ^ { \prime } = \frac { \ln x } { x y }$

question 64

Multiple Choice

Find the solution of the initial-value problem $y ^ { \prime } = \frac { \ln x } { x y }$ , $y ( 1 ) = 2$ .

• A) \(y = \frac { 1 + x } { 1 + \ln x }\)
• B) \(y = \frac { 8 x } { ( 1 + x ) ^ { 2 } }\)
• C) \(y = 2 + 2 \ln x\)
• D) \(y = \sqrt { 4 + ( \ln x ) ^ { 2 } }\)
• E) \(y = x \ln x + 2 x\)
• F) \(y = x \left( 1 + x ^ { 2 } \right)\)
• G) \(y = x + \sqrt { 1 + \ln x }\)
• H) \(y = \sqrt { x } ( 1 + x )\)

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