MathematicsMedium38×since 2002Q3630If the solution curve of the differential equation dydx=x+y−2x−y\frac{d y}{d x}=\frac{x+y-2}{x-y}dxdy=x−yx+y−2 passes through the points (2,1)(2,1)(2,1) and (k+1,2),k>0(\mathrm{k}+1,2), \mathrm{k}>0(k+1,2),k>0, thenA2tan−1(1k)=loge(k2+1)2 \tan ^{-1}\left(\frac{1}{k}\right)=\log _{e}\left(k^{2}+1\right)2tan−1(k1)=loge(k2+1)Btan−1(1k)=loge(k2+1)\tan ^{-1}\left(\frac{1}{k}\right)=\log _{e}\left(k^{2}+1\right)tan−1(k1)=loge(k2+1)C2tan−1(1k+1)=loge(k2+2k+2)2 \tan ^{-1}\left(\frac{1}{k+1}\right)=\log _{e}\left(k^{2}+2 k+2\right)2tan−1(k+11)=loge(k2+2k+2)D2tan−1(1k)=loge(k2+1k2)2 \tan ^{-1}\left(\frac{1}{k}\right)=\log _{e}\left(\frac{k^{2}+1}{k^{2}}\right)2tan−1(k1)=loge(k2k2+1)Check answerSkip