Differential Equations: JEE Main 2026 Mathematics question

Let $y=y(x)$ be the solution of the differential equation $\left(x^2-x\sqrt{x^2-1}\right)dy+\left(y\left(x-\sqrt{x^2-1}\right)-x\right)dx=0$, $x\ge1$. If $y(1)=1$, then the greatest integer less than $y(\sqrt5)$ is ________.