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AP EAMCET201923 Apr 2019Morning ShiftMathematicsDifferential EquationsActual

The solution of the differential equation (x d y d x =y-x ( y x ) ) is (Here, (k ) is an arbitrary constant)

Options

  1. A(x=y ⁻¹ ( k x ) )
  2. B(y=x ⁻¹ ( k x ) )
  3. C(x y+k=0 )
  4. D(y=x (k x) )

Correct answer

B. (y=x ⁻¹ ( k x ) )

Step-by-step solution

Given differential equation is ( aligned x d y d x & =y-x y x & d y d x = y x - ( y x ) aligned ) Let ( y=v x ) ( d y d x =v+x d v d x ) So, ( v+x d v d x =v- v d v v =- d x x ) ( v d v= (- 1 x ) d x ) ( | v|=- |x|+ k ) ( v= k x ) ( v= ⁻¹ ( k x ) y=x ⁻¹ ( k x ) ) Hence, option (b) is correct.

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