JEE Main 202431 Jan, Morning shiftMathematicsMediumDifferential Equations163× since 2002The solution curve of the differential equation ydxdy=x(logex−logey+1),x>0,y>0y \frac{d x}{d y}=x\left(\log _e x-\log _e y+1\right), x>0, y>0ydydx=x(logex−logey+1),x>0,y>0 passing through the point (e,1)(e, 1)(e,1) isAOption A. ∣logeyx∣=y2\left|\log _e \frac{y}{x}\right|=y^2logexy=y2BOption B. ∣logeyx∣=x\left|\log _e \frac{y}{x}\right|=xlogexy=xCOption C. ∣logexy∣=y\left|\log _e \frac{x}{y}\right|=ylogeyx=yDOption D. 2∣logexy∣=y+12\left|\log _e \frac{x}{y}\right|=y+12logeyx=y+1CheckSkip · show solution
