Let \( y=y(x) \) be the solution of the differential equation \( \left(x^2-x\sqrt{x^2-1}\right)\,dy+\left(y\left(x-\sqrt{x^2-1}\right)-x\right)\,dx=0,\ x\ge 1 \). If \( y(1)=1 \), then the greatest integer less than \( y(\sqrt{5}) \) is ______.
