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The general solution of the differential...

The general solution of the differential equaiton `(1+y^(2))dx+(1+x^(2))dy=0`, is

A

`x-y=c(1-xy)`

B

`x-y=c(1+xy)`

C

`x+y=c(1-xy)`

D

`x+y=c(1+xy)`

Text Solution

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The correct Answer is:
C
Given ` , (dx )/ ( 1 + x ^ 2 ) + ( dy ) /( 1 + y^ 2 ) = 0 `
` rArr tan ^( -1 ) x + tan ^( -1 ) y = tan ^( - 1 ) c ` [ integrating ]
` rArr ( x + y ) / ( 1- xy) = c `
` rArr x + y = c (1 -xy ) `
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