Homework Help: Basic Diffy Q

1. The problem statement, all variables and given/known data
[itex]dy/dx = 1/(x+y)[/itex]


2. Relevant equations
Errr. None that I know of.


3. The attempt at a solution
[itex]
v=x+y
[/itex]

[itex]
dy/dx=1/v
[/itex]

[itex]
dv/dx=1+dy/dx
[/itex]

[itex]
dv/dx=1+1/v
[/itex]

[itex]
dv/dx=(v+1)/v
[/itex]

[itex]
dv*v/(v+1)=dx
[/itex]

[itex]
v+1/(v+1) - 1/(v+1) = v/(v+1)
[/itex]

[itex]
\int 1\,dv - \int 1/(v+1)\,dv=\int 1\,dx
[/itex]

[itex]
v - \log (v+1) = x + C
[/itex]

[itex]
e^v/(v+1)=Ce^x
[/itex]

[itex]
e^(x+y)/(x+y+1)=Ce^x
[/itex]


I'm just wondering whether I can simplify this or maybe solve it another way so I can get y= (stuff)