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JEE Main20245 Apr 2024Evening ShiftMathematicsDifferential EquationsActual

The differential equation of the family of circles passing through the origin and having centre at the line y=x is :

Options

  1. A(x^2-y^2+2 x y ) d x= (x^2-y^2-2 x y ) d y
  2. B(x^2+y^2+2 x y ) d x= (x^2+y^2-2 x y ) d y
  3. C(x^2+y^2-2 x y ) d x= (x^2+y^2+2 x y ) d y
  4. D(x^2-y^2+2 x y ) d x= (x^2-y^2+2 x y ) d y

Correct answer

A. (x^2-y^2+2 x y ) d x= (x^2-y^2-2 x y ) d y

Step-by-step solution

aligned & C x^2+y^2+g x+g y=0....(1) & 2 x+2 y y^ +g+g y^ =0 & g=- ( 2 x+2 y y^ 1+y^ ) aligned Put in (1) aligned & x^2+y^2- ( 2 x+2 y y^ 1+y^ )(x+y)=0 & (x^2-y^2-2 x y ) y^ =x^2-y^2+2 x y aligned

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