JEE Main 20268 Apr, Evening shiftMathematicsEasyDifferential Equations163× since 2002Let y=y(x)y=y(x)y=y(x) be the solution of the differential equation x1−x2 dy+(y1−x2−xcos−1x)dx=0x\sqrt{1-x^2}\,dy+\left(y\sqrt{1-x^2}-x\cos^{-1}x\right)dx=0x1−x2dy+(y1−x2−xcos−1x)dx=0, x∈(0,1)x\in(0,1)x∈(0,1), limx→1−y(x)=1\lim_{x\to1^-}y(x)=1limx→1−y(x)=1. Then y(12)y\left(\frac{1}{2}\right)y(21) equals :AOption A. 3−π33-\frac{\pi}{\sqrt3}3−3πBOption B. 4−3 π4-\sqrt3\,\pi4−3πCOption C. 4−2π34-\frac{2\pi}{\sqrt3}4−32πDOption D. 3−π233-\frac{\pi}{2\sqrt3}3−23πCheckSkip · show solution
