If the solution curve of the differential equation \( \frac{d y}{d x}=\frac{x+y-2}{x-y} \) passe...

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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 \( (\mathrm{k}+1.2) \cdot k0 \), 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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