Differential Equations

If the solution curve, of the differential equation \(\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{x+y-2}{x-y}\) passing through the point \((2,1)\) is \(\tan ^{-1}\left(\frac{y-1}{x-1}\right)-\frac{1}{\beta} \log _{\mathrm{e}}\left(\alpha+\left(\frac{y-1}{x-1}\right)^2\right)=\log _{\mathrm{e}}|x-1|\), then \(5 \beta+\alpha\) is equal to __________.