If the solution curve of the differential equation (d y)/(d x)=(x+y-2)/(x-y) passes through the points (2,1) and (k+1,2), k>0, then

(A) 2 tan ⁻¹(1/k)= log e (k²+1)

(B) tan ⁻¹(1/k)= log e (k²+1)

(C) 2 tan ⁻¹(1/(k+1))= log e (k²+2 k+2)

(D) 2 tan ⁻¹(1/k)= log e ((k²+1)/(k²))

Differential Equations: JEE Main 2022 Mathematics question

JEE Main 2022 · 29 Jul, Evening shift · Q3630

JEE Main 202229 Jul, Evening shiftMathematicsMediumDifferential Equations163× since 2002

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}>0

, then

JEE Main 2022 · 29 Jul, Evening shift · Q3630

JEE Main 202229 Jul, Evening shiftMathematicsMediumDifferential Equations163× since 2002

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}>0

, then