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 ( {\k}+1,2), {\k} > 0, then [29-Jul-2022-Shift-2]

Correct Answer is : 2tan−1(1k)=loge(k2+1)

2 \tan ^{-1}(\frac{1}{k})=\log _e(k^2+1)

\tan ^{-1}(\frac{1}{k})-\log _e(k^2+1)

2 \tan ^{-1}(\frac{1}{k+1})=\log _e(k^2+2 k+2)

2 \tan ^{-1}(\frac{1}{k})=\log _e(\frac{k^2+1}{k^2})

JEE Mains 29-July-2022 Shift 2 Solved Paper

Section: Mathematics

Question : 9 of 90

Marks: +1, -0

If the solution curve of the differential equation ‌

=‌

x+y−2

x−y

passes through the points (2,1) and (k+1,2),k>0, then

[29-Jul-2022-Shift-2]

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