Solving dy/dx=(xy+y)/(x+xy) for y

[Queren Suriano]

Homework Statement

I have found this solution but I would like to solve for "Y" to write its general solution.

ln(y) +y = ln(x) + x +C

Relevant Equations

ln(y) +y = ln(x) + x +C
y=?

ln(y) +y = ln(x) + x +C
y=?

 

[fresh_42]

You will need Lambert's W-function for it, or go for some local solutions.