Let α|x|=|y| e^x y-β, α, β ∈ N be the solution of the differential equation x d y-y d x+x y(x d y+y d x)=0, y(1)=2. Then α+β is equal to ____

Let $\displaystyle \alpha|x|=|y| e^{x y-\beta}, \alpha, \beta \in \mathrm{N}$ be the solution of the differential equation $\displaystyle x \mathrm{~d} y-y \mathrm{~d} x+x y(x \mathrm{~d} y+y \mathrm{~d} x)=0$, $\displaystyle y(1)=2$. Then $\displaystyle \alpha+\beta$ is equal to $\displaystyle \_\_\_\_$