imo class 12 differential equations

Solve the homogeneous differential equation x dy/dx = y.

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#IMO#Class 12#Mathematics#Differential Equations#mathematical-reasoning

Solve the homogeneous differential equation x dy/dx = y.

  • A. y = Cx
  • B. y = C/x
  • C. xy = C
  • D. y = Cx²

Answer: A) y = Cx

Explanation: dy/dx = y/x. Separating variables: dy/y = dx/x. Integrating: log y = log x + log C → y = Cx.

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