Let y=y(x) be the solution of the differential equation: (d y)/(d x)+((6 x^2+(3 x^2+2 x^3+4) e^-2 x)/((x^3+2)(2+e^-2 x))) y=2+e^-2 x, x ∈(-1,2),…

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