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NDA2020MathematicsDifferential EquationsActual

The function u(x, y)=c which satisfies the differential equation x(d x-d y)+y(d y-d x)=0 , is

Options

  1. Ax^2+y^2=x y+c
  2. Bx^2+y^2=2 x y+c
  3. Cx^2-y^2=x y+c
  4. Dx^2-y^2=2 x y+c

Correct answer

B. x^2+y^2=2 x y+c

Step-by-step solution

x(d x-d y)+y(d y-d x)=0 On integrating both sides, we have aligned & x(d x-d y)+ y(d y-d x)=C( where C= constant ) & x^2 2 -x y+ y^2 2 -x y=C & x^2+y^2-2 x y=C & Or, x^2+y^2=2 x y+C aligned

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