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