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AP EAMCET202018 Sep 2020Morning ShiftMathematicsDifferential EquationsActual

The solution of the differential equation ( (x+y) d y=d x ) given that (y(0)=0 ) is

Options

  1. A(y= ( x+y 2 ) )
  2. B(y= ( x+y 2 ) )
  3. C(y= ( y 2 ) )
  4. D(y= ( x 2 ) )

Correct answer

A. (y= ( x+y 2 ) )

Step-by-step solution

Given differential equation ( (x+y) d y=d x d y d x = (x+y) ) Put (x+y=t 1+ d y d x = d t d x ) ( aligned & d t d x -1= (t) d t 1+ t = d x & t 1+ t d t= d x & (1- 1 1+ t ) d t= d x & [1- 1 2 ^2 ( t 2 ) ] d t= d x & t- ( t 2 )=x+c & x+y- ( x+y 2 )=x+c & y= ( x+y 2 )+c & f(0)=0 c=0 & y= ( x+y 2 ) aligned )

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