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Differential Equations question

2008 · Shift 2 · Q29

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PYQ Library
JEE Advanced
Mathematics
Differential Equations
2008 · Shift 2 · Q29

Differential Equations question

2008 · Shift 2 · Q29

JEE AdvancedMathematicsDifferential EquationsMCQ+3 / −1

Let a solution

y=y(x)

of the differential equation,

x\sqrt {{x^2} - 1} \,\,dy - y\sqrt {{y^2} - 1} \,dx = 0

satify

y\left( 2 \right) = {2 \over {\sqrt 3 }}.

STATEMENT-1 :

y\left( x \right) = \sec \left( {{{\sec }^{ - 1}}x - {\pi \over 6}} \right)

and STATEMENT-2 :

y\left( x \right)

given by

{1 \over y} = {{2\sqrt 3 } \over x} - \sqrt {1 - {1 \over {{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

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