Let a solution $y = y ( x )$ of the differential equation $$x \sqrt { x ^ { 2 } - 1 } d y - y \sqrt { y ^ { 2 } - 1 } d x = 0$$ satisfy $y ( 2 ) = \frac { 2 } { \sqrt { 3 } }$. STATEMENT-1 : $y ( x ) = \sec \left( \sec ^ { - 1 } x - \frac { \pi } { 6 } \right)$ and STATEMENT-2 : $y ( x )$ is given by $$\frac { 1 } { y } = \frac { 2 \sqrt { 3 } } { x } - \sqrt { 1 - \frac { 1 } { x ^ { 2 } } }$$ (A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True
Let a solution $y = y ( x )$ of the differential equation
$$x \sqrt { x ^ { 2 } - 1 } d y - y \sqrt { y ^ { 2 } - 1 } d x = 0$$
satisfy $y ( 2 ) = \frac { 2 } { \sqrt { 3 } }$.\\
STATEMENT-1 : $y ( x ) = \sec \left( \sec ^ { - 1 } x - \frac { \pi } { 6 } \right)$\\
and\\
STATEMENT-2 : $y ( x )$ is given by
$$\frac { 1 } { y } = \frac { 2 \sqrt { 3 } } { x } - \sqrt { 1 - \frac { 1 } { x ^ { 2 } } }$$
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1\\
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1\\
(C) STATEMENT-1 is True, STATEMENT-2 is False\\
(D) STATEMENT-1 is False, STATEMENT-2 is True