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dy/dx = (x + y - 2)/(x - y) through (2, 1)

The same question, asked 2 times: 29 Jul 2022, 27 Jan 2024. Every wording below, oldest first.

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  1. Question 1

    29 Jul 2022

    159
    If the solution curve of the differential equation dydx=x+y−2x−y\frac{dy}{dx}=\frac{x + y - 2}{x - y} passes through the point (2,1)(2,1) and (k+1,2),k>0(k + 1,2),k > 0, then

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  2. Question 2

    27 Jan 2024

    176
    If the solution curve, of the differential equation dydx=x+y−2x−y\frac{dy}{dx}=\frac{x + y - 2}{x - y} passing through the point (2,1)(2,1) is tan⁡−1(y−1x−1)−1βlog⁡e(α+(y−1x−1)2)=log⁡e∣x−1∣\tan^{- 1}\left( \frac{y - 1}{x - 1} \right)-\frac{1}{\beta}\log_{e}\left( \alpha +\left( \frac{y - 1}{x - 1} \right)^{2} \right)=\log_{e}|x - 1|, then 5β+α5\beta + \alpha is equal to