Solve the Initial-Value Problem $x y ^ { \prime } - y = x \ln x , \quad y ( 1 ) = 3$

question 51

Multiple Choice

Solve the initial-value problem.
$x y ^ { \prime } - y = x \ln x , \quad y ( 1 ) = 3$

• A) \(y ( x ) = 3 x ( \ln x ) ^ { 2 }\)
• B)
• \(y ( x ) = \frac { 1 } { 2 } x ( \ln x ) ^ { 2 } + 3 x\)
• C)
• \(y ( x ) = 3 x \ln x + \frac { 1 } { 2 } x\)
• D)
• \(y ( x ) = 3 \ln x + \frac { 1 } { 2 } x\)
• E)
• \(y ( x ) = \frac { 1 } { 2 } ( \ln x ) ^ { 3 } + x\)

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Definitions:

Open-Market Operations

The buying and selling of government securities by a central bank to control the money supply and interest rates.

Federal Reserve

The primary banking authority in the United States, tasked with overseeing monetary policy, managing bank regulation, and maintaining financial system stability.

Money Multiplier

The amount of money the banking system generates with each dollar of reserves.

Reserve Ratio

The fraction of deposits that banks hold as reserves.