JEE Main 202229 Jul, Morning shiftMathematicsMediumDifferential Equations163× since 2002Let the solution curve y=y(x)y=y(x)y=y(x) of the differential equation (1+e2x)(dy dx+y)=1\left(1+\mathrm{e}^{2 x}\right)\left(\frac{\mathrm{d} y}{\mathrm{~d} x}+y\right)=1(1+e2x)( dxdy+y)=1 pass through the point (0,π2)\left(0, \frac{\pi}{2}\right)(0,2π). Then, limx→∞exy(x)\lim\limits_{x \rightarrow \infty} \mathrm{e}^{x} y(x)x→∞limexy(x) is equal to :AOption A. π4\frac{\pi}{4}4πBOption B. 3π4\frac{3\pi}{4}43πCOption C. π2\frac{\pi}{2}2πDOption D. 3π2\frac{3\pi}{2}23πCheckSkip · show solution
