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Which one of the following is the general solution of the first order differential equation $$\frac{dy}{dx}=(x+y-1)^{2},$$ where $x,y$ are real?

  1. $y=1+x+\tan^{-1}(x+c)$, where $c$ is a constant
  2. $y=1+x+\tan(x+c)$, where $c$ is a constant
  3. $y=1-x+\tan^{-1}(x+c)$, where $c$ is a constant
  4. $y=1-x+\tan(x+c)$, where $c$ is a constant
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