Let f(x)=x−1 and g(x)=e^x... | Differential Equations

JEE MAIN 2025

08-04-25 S2

Question

Let $f(x)=x-1$ and $g(x)=e^x$ for $x \in \mathbb{R}$. If $\frac{d y}{d x}=\left(e^{-2 \sqrt{x}} g(f(f(x)))-\frac{y}{\sqrt{x}}\right), y(0)=0$, then $y(1)$ is

Select the correct option:

$\frac{2 e-1}{e^3}$

$\frac{e-1}{e^4}$

$\frac{1-e^3}{e^4}$

$\frac{1-e^2}{e^4}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Medium

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