The Qs is to solve the differential equation:

$\displaystyle \frac{dy}{dx} = \frac{(x+y)}{(x-y)}$ with y(1) = 1

I have tried to use Homogeneous differential equation rules:

$\displaystyle \frac{dy}{dx} = H(\frac{y}{x})$

Then $\displaystyle y(x) = xu(x); x\frac{du}{dx} + y = H(u)$

Relative to the real Qs, my step is shown below

$\displaystyle \frac{dy}{dx} = \frac{x+y}{x-y} = .... = \frac{1}{1-\frac{y}{x}} + \frac{1}{[\frac{1}{(\frac{y}{x})}-1]} = H(\frac{y}{x})$

By Homogeneous differential equation rules

I got $\displaystyle \frac{du}{dx} = \frac{1+u^2}{(1-u)x}$

and after I antidifferentiate this equation

$\displaystyle arctan(u) - 0.5log(1+u^2) = log|x|+C$

after that, I don't know how to continue, please help!