Let a solution y = y(x)of the differential equation x√(x^2 - 1) dy - y√(y^2 - 1) dx = 0 satisfy y(2) = 2/√3

Question

For the following questions, choose the correct answer from the codes (a), (b), (c) and (d) defined as follows.

(a) Statement I is true, Statement II is also true;

Statement II is the correct explanation of Statement I.

(b) Statement I is true, Statement II is also true;

Statement II is not the correct explanation of Statement I.

(c) Statement I is true; Statement II is false.

(d) Statement I is false; Statement II is true.

Let a solution y = y(x) of the differential equation x√(x² - 1) dy - y√(y² - 1) dx = 0 satisfy y(2) = 2/√3 

Statement I : y(x) = sec(sec^-1 x - π/6) and 

Statement II : y(x) is given by 1/y = 2√3/x - √(1 - 1/x²)

Answer 1

Correct option : (c) Statement I is true; Statement II is false.

Given,