Let y=y(x) be the solution of the differential equation x d y-y d x=√((x^2-y^2)) d x, x ≥ 1, with y(1)=0. If the area bounded by the line x=1, x=…

Let $\displaystyle y=y(x)$ be the solution of the differential equation $\displaystyle x \mathrm{~d} y-y \mathrm{~d} x=\sqrt{\left(x^2-y^2\right)} \mathrm{d} x, x \geqslant 1$, with $\displaystyle y(1)=0$. If the area bounded by the line $\displaystyle x=1, x=\mathrm{e}^\pi, y=0$ and $\displaystyle y=y(x)$ is $\displaystyle \alpha \mathrm{e}^{2 \pi}+\beta$, then the value of $\displaystyle 10(\alpha+\beta)$ is equal to \_\_\_\_.