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AP EAMCET2005MathematicsDifferential Equations

If d x+d y=(x+y)(d x-d y), then (x+y) is equal to

Options

  1. Ax+y+c
  2. Bx+2y+c
  3. Cx-y+c
  4. D2 x+y+c

Correct answer

C. x-y+c

Step-by-step solution

Given that d x+d y=(x+y)(d x-d y) d x(x+y-1)=d y(x+y+1) Let x+y=t d y d x = d t d x -1 From Eq. (i) aligned d t d x -1 & = t-1 t+1 d t d x & = t-1+t+1 t+1 (t+1) 2 t d t & =d x 1 2 (1+ 1 t ) d t & =d x aligned On integrating both sides, we get aligned 1 2 (t+ t) & =x+ C 2 (x+y) & =2 x-x+y+C (x+y) & =x-y+C aligned

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