Let a solution y = y ( x ) of the differential equation x x^ 2 -1 d y-y y^ 2 -1 d x=0…
Mathematics · JEE Advanced · NTA Exams — Differential Equations
Let a solution y = y(x) of the differential equation
\(x \sqrt{x^{2}-1} d y-y \sqrt{y^{2}-1} d x=0\)satisfies \(y(2)=\frac{2}{\sqrt{3}} .\)
Statement - 1 : \(y(x)=\sec \left(\sec ^{-1} x-\frac{\pi}{6}\right)\)
Statement - 2 : y(x) is given by
\(x \sqrt{x^{2}-1} d y-y \sqrt{y^{2}-1} d x=0\)satisfies \(y(2)=\frac{2}{\sqrt{3}} .\)
Statement - 1 : \(y(x)=\sec \left(\sec ^{-1} x-\frac{\pi}{6}\right)\)
Statement - 2 : y(x) is given by
- Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation of Statement-1
- Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
- Statement-1 is True, Statement-2 is False
- Statement-1 is False, Statement-2 is True.
Answer
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation of Statement-1
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