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Differential Equations question

2022 · 29 Jul · Shift 2 · Q29

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JEE Main
Mathematics
Differential Equations
2022 · 29 Jul · Shift 2 · Q29

Differential Equations question

2022 · 29 Jul · Shift 2 · Q29

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

If the solution curve of the differential equation

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

passes through the points

(2,1)

and

(\mathrm{k}+1,2), \mathrm{k}\gt 0

, then

A
$2 \tan ^{-1}\left(\frac{1}{k}\right)=\log _{e}\left(k^{2}+1\right)$
B
$\tan ^{-1}\left(\frac{1}{k}\right)=\log _{e}\left(k^{2}+1\right)$
C
$2 \tan ^{-1}\left(\frac{1}{k+1}\right)=\log _{e}\left(k^{2}+2 k+2\right)$
D
$2 \tan ^{-1}\left(\frac{1}{k}\right)=\log _{e}\left(\frac{k^{2}+1}{k^{2}}\right)$

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