# Unfamiliar Equation

Calculus Level 5

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

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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