JEE Main 20231 Feb, Evening shiftMathematicsMediumDifferential Equations163× since 2002Let αx=exp(xβyγ)\alpha x=\exp \left(x^{\beta} y^{\gamma}\right)αx=exp(xβyγ) be the solution of the differential equation 2x2y dy−(1−xy2)dx=0,x>0,y(2)=loge22 x^{2} y \mathrm{~d} y-\left(1-x y^{2}\right) \mathrm{d} x=0, x > 0,y(2)=\sqrt{\log _{e} 2}2x2y dy−(1−xy2)dx=0,x>0,y(2)=loge2. Then α+β−γ\alpha+\beta-\gammaα+β−γ equals :AOption A. 1BOption B. 0COption C. 3DOption D. −1-1−1CheckSkip · show solution
