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Solve: `[(x+1)y/x+siny]dx+[x+log_(e)x+xcosy]dy=0`

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Solve: `[(x+1)y/x+siny]dx+[x+log_(e)x+xcosy]dy=0`
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We can rewrite the given equation as
`(ydx+xdy)+(y/xdx+log_(e)xdy)+(sinydx+xcosydy)=0`
`rArr d(xy)=(yd(log_(e)x)+log_(e)xdy)+(sinydx+xd(siny))=0`
`rArr d(xy)+d(ylog_(e)x) + d(xsiny)=0`
Integrating both the sides, we get
`xy+ylog_(e)x+xsiny=C`
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