JEE Main 20241 Feb, Morning shiftMathematicsMediumDifferential Equations163× since 2002Let y=y(x)y=y(x)y=y(x) be the solution of the differential equation dy dx=2x(x+y)3−x(x+y)−1,y(0)=1\frac{\mathrm{d} y}{\mathrm{~d} x}=2 x(x+y)^3-x(x+y)-1, y(0)=1 dxdy=2x(x+y)3−x(x+y)−1,y(0)=1. Then, (12+y(12))2\left(\frac{1}{\sqrt{2}}+y\left(\frac{1}{\sqrt{2}}\right)\right)^2(21+y(21))2 equals :AOption A. 44+e\frac{4}{4+\sqrt{\mathrm{e}}}4+e4BOption B. 33−e\frac{3}{3-\sqrt{\mathrm{e}}}3−e3COption C. 21+e\frac{2}{1+\sqrt{\mathrm{e}}}1+e2DOption D. 12−e\frac{1}{2-\sqrt{\mathrm{e}}}2−e1CheckSkip · show solution
