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MCQMediumJEE Main 2025 · 8 April, Shift 2Linear Differential Equations

Mathematics Question from JEE Main 2025 · 8 April, Shift 2

Let f(x)=x−1f(x) = x - 1 and g(x)=exg(x) = e^x for x∈Rx \in \mathbb{R}. If

dydx=(e−2xg(f(f(x)))−yx),  y(0)=0,\frac{dy}{dx} = \left( e^{-2\sqrt{x}} g\left(f\left(f(x)\right)\right) - \frac{y}{\sqrt{x}} \right), \; y(0) = 0,

then y(1)y(1) is

  • A

    2e−1e3\frac{2e-1}{e^3}

  • B

    1−e2e4\frac{1-e^2}{e^4}

  • C

    e−1e4\frac{e-1}{e^4}

  • D

    1−e3e4\frac{1-e^3}{e^4}

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