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Question

The general solution of the differential equation (1+y2)dx+(1+x2)dy=0 is

A
xy=C(1xy)
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B
xy=C(1+xy)
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C
x+y=C(1xy)
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D
x+y=C(1+xy)
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Solution

The correct option is C x+y=C(1xy)
(1+y2)dx+(1+x2)dy=0
dx1+x2+dy1+y2=0
On integrating, we get
tan1x+tan1y=C
x+y1xy=C
x+y=C(1xy) is the required solution.

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