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MHT CET20227 Aug 2022Morning ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation x^2+y^2-2 x y d y d x =0 is (where C is a constant of integration.)

Options

  1. A2 (x^2-y^2 )+x=C
  2. Bx^2+y^2=C x
  3. Cx^2-y^2=C x
  4. Dx^2+y^2=C y

Correct answer

C. x^2-y^2=C x

Step-by-step solution

aligned & x^2+y^2-2 x y d y d x =0 d y d x = x^2+y^2 2 x y v+x d v d x = 1+v^2 2 v & [Let y=n x] & 2 v d v 1-v^2 = d x x & - |1-v^2 |+ |c|= |x| & | c 1-v^2 |= |x| & c 1- y^2 x^2 =x & c x=x^2-y^2 aligned

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