Solve the equation `(x+y+1)((dy)/(dx))=1`

Answer

`x=ce^(y)-y-2`

Explanation

The given equation can be rewritten as
`(dx)/(dy) -1x=(y+1)` [linear, y as independent variable]
Here, `P=-1, Q=(y+1)`
`I.F. = e^(int(-dy))=e^(-y)`
Therefore, the solution is
`xe^(-y)=int(y+1)e^(-y)dy+c`
or `x=ce^(y)-y-2`