JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumDifferential Equations163× since 2002Let f(x)=x−1f(x) = x - 1f(x)=x−1 and g(x)=exg(x) = e^xg(x)=ex for x∈Rx \in \mathbb{R}x∈R. If dydx=(e−2xg(f(f(f(x))))−yx),y(0)=0,\frac{dy}{dx} = \left( e^{-2\sqrt{x}} g(f(f(f(x)))) - \frac{y}{\sqrt{x}} \right), \quad y(0) = 0,dxdy=(e−2xg(f(f(f(x))))−xy),y(0)=0, then y(1)y(1)y(1) is:AOption A. 1−e2e4\frac{1 - e^2}{e^4}e41−e2BOption B. 2e−1e3\frac{2e - 1}{e^3}e32e−1COption C. e−1e4\frac{e - 1}{e^4}e4e−1DOption D. 1−e3e4\frac{1 - e^3}{e^4}e41−e3CheckStep-by-step hintSkip · show solution
