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AP EAMCET202422 May 2024Morning ShiftMathematicsDifferential EquationsActual

The general solution of the differential equation x d y-y d x= x^2+y^2 d x is

Options

  1. Ay+ x^2+y^2 =c x^2
  2. By+ x^2+y^2 =c x
  3. Cx+ x^2+y^2 =c y
  4. Dx- x^2+y^2 =c y^2

Correct answer

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

Step-by-step solution

x d y-y d x= x^2+y^2 d x Dividing by x d x both sides d y d x = y x + 1+ y^2 x^2 Let y=v x d y d x =v+x d v d x Hence, v+x d v d x =v+ 1+v^2 aligned & x d v d x = 1+v^2 d v 1+v^2 = d x x & (v+ 1+v^2 )= x+ c & y x + 1+ y^2 x^2 =c x y+ x^2+y^2 =c x^2 . aligned

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