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AP EAMCET2014MathematicsDifferential Equations

The solution of y+(x y-1) d y d x =0 is

Options

  1. Ax y= y+C
  2. By- y=C x
  3. Cy+ y=C x
  4. Dx y+ y=C

Correct answer

A. x y= y+C

Step-by-step solution

Given differential equation can be rewritten as aligned & y d y d x +x y-1=0 & d x d y +( y) x= y & aligned It is a linear differential equation of the form aligned d x d y +P x & =Q I F & =e^ P d y =e^ y d y & =e^ y = y aligned Solution is aligned & x y= ^2 y d y & x y= y+C & aligned

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