Solving a Differential Equation using variable seperable method

Question

I am learning differential equations and was solving differential equations using Variable Seperable Method when I got stuck on this problem :

$$(x+y)dx+dy=0$$

No,I cannot seperate the functions to the form $M(x)dx=N(y)dy$..

How should I proceed further using variable seperable method?

I am new to latex so please forgive me for any mistake commited.

Answer 1

Hint

Let $y+x=z \implies y=z-x\implies y'=z'-1$ making the equation $$z'+z=1$$ which is easy to solve.

Answer 2

$ dy/dx = - y - x $

$ dy/ dx + y = -x $

integral factor is $( e^ x)$ (liner diffrential equation)

$Ye^x = \int ( -xe^ x)dx$

$ Ye^x= - [xe ^ x - ( e^ x ) ] + c $