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AP EAMCET2006MathematicsDifferential Equations

The solution of (x^2+y^2 ) d x=2 x y d y is :

Options

  1. Ac (x^2-y^2 )=x
  2. Bc (x^2+y^2 )=x
  3. Cc (x^2-y^2 )=y
  4. Dc (x^2+y^2 )=y

Correct answer

A. c (x^2-y^2 )=x

Step-by-step solution

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

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