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Differential Equations question

2024 · 27 Jan · Shift 2 · Q60

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JEE Main
Mathematics
Differential Equations
2024 · 27 Jan · Shift 2 · Q60

Differential Equations question

2024 · 27 Jan · Shift 2 · Q60

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

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)

is

\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

\underline{\hspace{2cm}}

.

Numerical answer

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