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 (α+((y-1)/(x-1))²)= log e |x-1|, then 5 β+α is equal to _ _ _ _ _.

Differential Equations: JEE Main 2024 Mathematics question

JEE Main 2024 · 27 Jan, Evening shift · Q33

JEE Main 202427 Jan, Evening shiftMathematicsMediumDifferential Equations163× since 2002

If the solution curve, of the differential equation

\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{x+y-2}{x-y}

passing through the point

(2,1)

\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

5 \beta+\alpha

is equal to __________.

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