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MHT CET202313 May 2023Evening ShiftMathematicsDifferential EquationsActual

The solution of (1+x y) y ~d x+(1-x y) x ~d y=0 is.

Options

  1. A( x y )+ 1 x y = k , where k is constant of integration.
  2. B( x y )= 1 x y + k , where k is constant of integration.
  3. C( x y )+x y= k , where k is constant of integration.
  4. D( x y )=x y+ k , where k is constant of integration.

Correct answer

B. ( x y )= 1 x y + k , where k is constant of integration.

Step-by-step solution

(1+x y) y ~d x+(1-x y) x ~d y=0 y ~d x+x ~d y+x y^2 ~d x-x^2 y ~d y=0 y ~d x+x ~d y x^2 y^2 + d x x - d y y =0 d (x y) x^2 y^2 + d x x - d y y =0 Integrating on both sides, we get - 1 x y + x- y= k ( x y )= 1 x y + k

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