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AP EAMCET202419 May 2024Evening ShiftMathematicsDifferential EquationsActual

The solution of x d y-y d x= x^2+y^2 d x when y( 3 )=1 is

Options

  1. Ay^2+ x^2+y^2 =x^2
  2. B5 y- x^2+y^2 =x^2
  3. Cy+ x^2+y^2 =x
  4. D5 y^2- x^2+y^2 =x

Correct answer

C. y+ x^2+y^2 =x

Step-by-step solution

Since, x d y-y d x= x^2+y^2 d x aligned & x d y= (y+ x^2+y^2 ) d x & d y d x = y+ x^2+y^2 x aligned Let y=v x d y d x =v+x d v d x So, v+x d v d x = v x+ x^2+v^2 x^2 x aligned & x d v d x = 1+v^2 d v 1+v^2 = 1 x d x & (v+ v^2+1 )= x c & y+ x^2+y^2 =xc aligned Since, y( 3 )=1 1+ 4 =3 c c=1 So, y+ x^2+y^2 =x

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