If the solution curve of the differential equation $\frac{dy}{dx} = \frac{x + y - 2}{x - y}$ passes through the point $(2, 1)$ and $(k + 1, 2)$, $k > 0$, then\\
(1) $2\tan^{-1}\left(\frac{1}{k}\right) = \log_e(k^2 + 1)$\\
(2) $\tan^{-1}\left(\frac{1}{k}\right) = \log_e(k^2 + 1)$\\
(3) $2\tan^{-1}\left(\frac{1}{k+1}\right) = \log_e(k^2 + 2k + 2)$\\
(4) $2\tan^{-1}\left(\frac{1}{k}\right) = \log_e\frac{k^2 + 1}{k^2}$