How does one solve the differential equation dy over dx equals x plus y?

treat x+y as a variable u.
dy/dx=u
dy=udx
u=x+y
du/dx=1+dy/dx
du/dx=1+x+y
du/dx=1+u
du/(1+u)=dx
dy=[u/(1+u)]du
y+C=u-ln(u+1)
y+C=x+y=ln(x+y+1)
-x+C=ln(x+y+1)
Ce-x=x+y+1
Ce-x-x-1=y