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AP EAMCET202420 May 2024Morning ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation (x+y) y d x+(y-x) x d y=0 is

Options

  1. Ax+y (c y)=0
  2. By x = (x y)+c
  3. Cx+y (c x y)=0
  4. Dy x = (c x y)

Correct answer

C. x+y (c x y)=0

Step-by-step solution

y=v x d y d x =v+x d v d x (x+y) y d x=(x-y) x d y d y d x = (x+y) y (x-y) x v+x d v d x = (x+v x) v x (x-v x) x = v^2+v 1-v x d v d x = v^2+v 1-v -v= 2 v^2 1-v ( 1-v v^2 ) d v= 2 x d x -1 v - v=2 x+c- x y - y+ x=2 x+c - x y = (c^ x y )x+y (c^ x y )=0

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