Let a solution y=y(x) of the differential equation x x^ 2 -1 d y-y y^ 2 -1 d x=0 satisfy…
Mathematics · JEE Main · NTA Exams — Differential Equations
Let a solution \(y=y(x)\) of the differential equation \(x \sqrt{x^{2}-1} d y-y \sqrt{y^{2}-1} d x=0\) satisfy \(y(2)=\) \(\frac{2}{\sqrt{3}} .\)
Statement - 1 : \(y(x)=\) \(\text { sec }\) \(\left(\sec ^{-1} x-\frac{\pi}{6}\right)\)
Statement - 2 : \(y(x)\) is given by \(\frac{1}{y}=\frac{2 \sqrt{3}}{x}-\sqrt{1-\frac{1}{x^{2}}}\)
- Both Statements are true and Statement - 2 is the correct explanation for Statement - 1
- Both Statements are true but Statement - 2 is not a correct explanation for Statement - 1
- Statement - 1 is true and Statement - 2 false
- Statement - 1 is false and Statement - 2 is true
Answer
(D) Statement - 1 is false and Statement - 2 is true
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- Solution of the differential equation y (2 x^ 4 +y ) d y d x = (1-4 x y^ 2 ) x^ 2 is given by :
- The solution of the differential equation d y d x = 3 x^ 2 y^ 4 +2 x y x^ 2 -2 x^ 3 y^ 3 is,
- The solution of Differential equation d y d x = x+2 y-3 2 x+y-3 is
- The solution of (cosec x log y)dy + (x 2 y)dx=0 is -
- The integrating factor of the differentiable equation (xy – 1) dy dx + y ^ 2 =0 is
- The general solution of y^ 2 d x+ (x^ 2 -x y+y^ 2 ) d y=0 is,
- The curve amongst the family of curves represented by the differential equation, (x^ 2 -y^ 2 ) d x+2 x y d…
- The general solution of the differential equation [2 x y -x] dy + y dx = 0 is
More Differential Equations questions · Browse all practice questions