- #1

domesticbark

- 6

- 0

## Homework Statement

[itex]dy/dx = 1/(x+y)[/itex]

## Homework Equations

Errr. None that I know of.

## 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)