I am trying to solve: $\displaystyle (2*-x*\frac{dy}{dx}) +(\frac{dy}{dx})-{y(x)}-1=0$ and I seem to be missing a step: when I solve this i get y = 1 which doesn't seem right. Thank you for your help
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This can be re-written as $\displaystyle \displaystyle \frac{dy}{dx}(1-2x)=y+1$ which is separable. It becomes $\displaystyle \displaystyle \frac{dy}{y+1}= \frac{dx}{1-2x}$
It's also first order linear if written as $\displaystyle \displaystyle \frac{dy}{dx} + \frac{1}{2x - 1}\,y = -\frac{1}{2x-1}$ and so you can use the Integrating Factor Method...
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