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y(xy+1)dx+x(1+xy+x^(2)y^(2))dy=0...

`y(xy+1)dx+x(1+xy+x^(2)y^(2))dy=0`

Text Solution

Verified by Experts

The correct Answer is:
`-1/(2x^(2)y^(2))-1/(xy)+2log_(e)y=c`
`y(xy+1)dx+x(1+xy+x^(2)y^(2))dy=0`
`therefore (xy^(2)x+x^(2)ydy)+(ydx+xdy)+x^(3)y^(2)dy=0`
`rArr xyd(xy)+d(xy)+x^(3)y^(2)dy=0`
`rArr (d(xy))/(x^(3)y^(3))+(d(xy))/(x^(2)y^(2))+(dy)/(y)=0`
`rArr -1/(2x^(2)y^(2))-1/(xy) +log_(e)y=c`
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