Q89. Let $\alpha | x | = | y | \mathrm { e } ^ { x y - \beta } , \alpha , \beta \in \mathbf { N }$ be the solution of the differential equation $x \mathrm {~d} y - y \mathrm {~d} x + x y ( x \mathrm {~d} y + y \mathrm {~d} x ) = 0$, $y ( 1 ) = 2$. Then $\alpha + \beta$ is equal to $\_\_\_\_$\\