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The solution of the differential equation fraction numerator d y over denominator d x end fraction equals y over x plus fraction numerator ϕ open parentheses y over x close parentheses over denominator ϕ to the power of straight prime open parentheses y over x close parentheses end fraction is

  1. ϕ open parentheses fraction numerator y over denominator x end fraction close parentheses equals k x    
  2. x ϕ open parentheses fraction numerator y over denominator x end fraction close parentheses equals k    
  3. ϕ open parentheses fraction numerator y over denominator x end fraction close parentheses equals k y    
  4. y ϕ open parentheses fraction numerator y over denominator x end fraction close parentheses equals k    

The correct answer is: ϕ open parentheses fraction numerator y over denominator x end fraction close parentheses equals k x

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