The curve passing through the point (1,1) satisfies the differential equation dydx+√(x2−1)(y2−1)xy=0. If the curve passes through the point (√2,k), then the largest value of |[k]| is (where, [.] represents the greatest integer function)

The curve passing through the point (1,1) satisfies the differential e

1.	The curve passing through the point (1,1) satisfies the differential equation dydx+√(x2−1)(y2−1)xy=0. If the curve passes through the point (√2,k), then the largest value of \|[k]\| is (where, [.] represents the greatest integer function)
Answer» The curve passing through the point $(1, 1)$ satisfies the differential equation $\frac{d y}{d x} + \frac{\sqrt{(x^{2} - 1) (y^{2} - 1)}}{x y} = 0$ . If the curve passes through the point $(\sqrt{2}, k)$ , then the largest value of $\| [k] \|$ is (where, $[.]$ represents the greatest integer function)