Find the general solution of the differential equations:`(x+y)(dx)/(dy)=1`

Explanation

`(x+y)(dy)/(dx)=1implies(dx)/(dy)=x+y`
`implies (dx)/(dy)-x=y`
Here, `P=-1`, `Q=y`
I.F.`=e^(intPdy)=e^(int-1dy)=e^(-y)`
and general solution : `x(e^(-y))=intye^(-y)dy+c`
`implies xe^(-y)=y(-e^(-y))-int1(-e^(-y))dy+c`
`=-ye^(-y)-e^(-y)+c`
`implies x=-y-1+ce^(y)`
`implies x+y+1=ce^(y)`