JEE Math Practice Question

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

1. A.$\frac{1 - e^3}{e^4}$
2. B.$\frac{e-1}{e^4}$
3. C.$\frac{1 - e^2}{e^4}$
4. D.$\frac{2e - 1}{e^3}$