Differential Equations: JEE Main 2026 Mathematics question

Let $y=y(x)$ be the solution of the differential equation: $\frac{dy}{dx}+\left(\frac{6x^2+\left(3x^2+2x^3+4\right)e^{-2x}}{\left(x^3+2\right)\left(2+e^{-2x}\right)}\right)y=2+e^{-2x}$, $x\in(-1,2)$, satisfying $y(0)=\frac32$. If $y(1)=\alpha(2+e^{-2})$, then $\alpha$ is equal to: