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