\[2 \dfrac{d^2y}{dx^2} + 3 \dfrac{dy}{dx} + y = e^{-3x} , \quad x \in \mathbb{R} \]

Let \( y \colon \mathbb{R} \to \mathbb{R} \) be a solution of the above ordinary differential equation, satisfying \(\displaystyle\lim_{x\rightarrow \infty} e^xy(x) = 0\). Find \(y(0)\).

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