If the solution curve of the differential equation dy/dx = (x + y… | JEE Main 2024 Mathematics PYQ

NVAMediumJEE Main 2024 · 27 January, Shift 2Separation of Variables

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

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