Let y=y(x) be the solution of the differential equation (x^2-x √(x^2-1)) d y+(y(x-√(x^2-1))-x) d x=0, x ≥ 1. If y(1)=1, then the greatest integer…

Let $\displaystyle y=y(x)$ be the solution of the differential equation $\displaystyle \left(x^2-x \sqrt{x^2-1}\right) d y+\left(y\left(x-\sqrt{x^2-1}\right)-x\right) d x=0, x \geq 1$. If $\displaystyle y(1)=1$, then the greatest integer less than $\displaystyle y(\sqrt{5})$ is $\displaystyle \_\_\_\_$.