If the solution curve, of the differential equation \(\displaystyle \frac{dy}{dx}=\frac{x+y-2}{x-y} \) passing through the point \( (2,1) \) is
\(\displaystyle \tan^{-1}\!\left(\frac{y-1}{x-1}\right)-\frac{1}{\beta}\log_{e}\!\left(a+\left(\frac{y-1}{x-1}\right)^{2}\right)=\log_{e}|x-1|, \) then \( 5\beta+\alpha \) is equal to:
