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Question

Solution of the equation (1+x2)dy=(1+y2)dx is 
  1. y – x = c(1 + xy)
  2. y– x = c(1 – xy)
  3. tan1y=tan1x+c
  4. tan1x+cot1y=c


Solution

The correct options are
A y – x = c(1 + xy)
C tan1y=tan1x+c
D tan1x+cot1y=c
dx1+y2=dx1+x2
or tan1y=tan1+c   (c is correct)
or π2cot1y=tan1x+c
or tan1x+cot1y=π2c (d is correct)
also tan1ytan1x=c
tan1(yx1+xy)=cyx1+xy=tanc=k (a is correct)

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