The general solution of the differential equation $\frac{dy}{dx} + y = 1$ ($y \neq 1$) is:
$\log \left| \frac{1}{1-y} \right| = x + c$
$\log \left| 1-y \right| = x + c$
$\log \left| 1+y \right| = x + c$
$\log \left| \frac{1}{1-y} \right| = -x + c$
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