The solution of differential equation (ex+1)ydy=(y+1)exdx is
A
(ex+1)(y+1)=Cey
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B
(ex+1)|(y+1)|=Ce−y
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C
(ex+1)(y+1)=±Cey
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D
None of these
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Solution
The correct option is A(ex+1)(y+1)=Cey The given differential equation is (ex+1)⋅ydy=(y+1)exdx ⇒ydy(y+1)=ex(ex+1)dx ⇒(y+1−1y+1)dy=exex+1dx ⇒dy−1y+1dy=exex+1dx On integrating, we get ⇒y−log|y+1|=log(ex+1)+logk ⇒y=log|(y+1)(ex+1)|k ⇒(y+1)(ex+1)=eyC.