Let \( y = y(x) \) be the solution of the differential equation:
\( \dfrac{dy}{dx} + \left( \dfrac{6x^2 + (3x^2 - 2x^3 - 4)e^{-2x}}{(x^3 + 2)(2 + e^{-2x})} \right) y = 2 + e^{-2x}, \; x \in (-1, 2), \) satisfying \( y(0) = \dfrac{3}{2} \). If \( y(1) = \alpha(2 + e^{-2}) \), then \( \alpha \) is equal to:
