JEE Main 20248 Apr, Morning shiftMathematicsMediumDifferential Equations163× since 2002Let y=y(x)y=y(x)y=y(x) be the solution of the differential equation (1+y2)etanxdx+cos2x(1+e2tanx)dy=0,y(0)=1(1+y^2) e^{\tan x} d x+\cos ^2 x(1+e^{2 \tan x}) d y=0, y(0)=1(1+y2)etanxdx+cos2x(1+e2tanx)dy=0,y(0)=1. Then y(π4)y\left(\frac{\pi}{4}\right)y(4π) is equal toAOption A. 1e2\frac{1}{e^2}e21BOption B. 2e2\frac{2}{e^2}e22COption C. 2e\frac{2}{e}e2DOption D. 1e\frac{1}{e}e1CheckSkip · show solution
