Differential Equations: JEE Main 2021 Mathematics question

Let y = y(x) be the solution of the differential equation xdy $-$ ydx = $\sqrt {({x^2} - {y^2})} dx$, x $\ge$ 1, with y(1) = 0. If the area bounded by the line x = 1, x = e^$\pi$, y = 0 and y = y(x) is $\alpha$e²$\pi$ + $\beta$, then the value of 10($\alpha$ + $\beta$) is equal to __________.