If the solution curve, of the differential equation (d y)/(d x)=(x+y-2)/(x-y) passing through the point (2,1) is tan^-1((y-1)/(x-1))-1/(β) log_e…

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