1. ## First Order ODE

I am trying to solve:

$(2*-x*\frac{dy}{dx}) +(\frac{dy}{dx})-{y(x)}-1=0$

and I seem to be missing a step: when I solve this i get y = 1 which doesn't seem right.

2. This can be re-written as $\displaystyle \frac{dy}{dx}(1-2x)=y+1$ which is separable.
It becomes $\displaystyle \frac{dy}{y+1}= \frac{dx}{1-2x}$
$\displaystyle \frac{dy}{dx} + \frac{1}{2x - 1}\,y = -\frac{1}{2x-1}$