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The general solution of the differential equation (x+y) d y d x =1 is

Options

  1. Ay= (x+y)+c
  2. By= (x+y)+c
  3. Cy= ( x+y 2 )+c
  4. Dy= ( x+y 2 )+c

Correct answer

C. y= ( x+y 2 )+c

Step-by-step solution

(x+y) d y d x =1 Put x+y=V 1+ d y d x = d V d x aligned & V ( dV dx -1 )=1 V ( dV dx )=1+ V & V 1+ V dV = dx & [ 1+ V 1+ V - 1 1+ V ] dV & = dx dV - 1 2 ^2 V 2 dV = dx aligned aligned & V - 1 2 ( V 2 ) ( 1 2 ) = x + c V - ( V 2 )= x + c & x + y - ( x + y 2 )= x + c & y = ( x + y 2 )+ c aligned

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