If $y=y(x)$ is the solution of the differential equation $\frac{d y}{d x}+\frac{4 x}{\left(x^2-1\right)} y=\frac{x+2}{\left(x^2-1\right)^{5 / 2}}, x>1$ such that $\mathrm{y}(2)=\frac{2}{9} \log _{\mathrm{e}}(2+\sqrt{3})$ and $\mathrm{y}(\sqrt{2})=\alpha \log _{\mathrm{e}}(\sqrt{\alpha}+\beta)+\beta-\sqrt{\gamma}, \alpha, \beta, \gamma \in \mathrm{N}$, then $\alpha \beta \gamma$ is equal to $\_\_\_\_$ .