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Question

The solution of the differential equation dydx=1+x+y+xy is


A

log(1+y)=x+x22+c

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B
(1+y)2=x+x22+c
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C
log(1+y)=log(1+x)+c
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D

None of these

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Solution

The correct option is A

log(1+y)=x+x22+c


dydx=1+x+y+xydydx=(1+x)(1+y)dy1+y=(1+x)dx
On integrating, we get
log (1+y)=x22+x+c.


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