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in Differential equations by (33.0k points)

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

Assertion (A): y = (x) = sec(sec–1x – (π/6)) 

Reason (R): y(x) is given by 1/y = (2√3/x) – √(1 – (1/x2))  

(a) Both A and R are true and R is the correct explanation of A. 

(b) Both A and R are true but R is not the correct explanation of A. 

(c) A is true and R is false. 

(d) A is false and R is true.

1 Answer

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Best answer

Answer is (c) A is true and R is false

Explanation :

The given differential equation is

x√(x2 – 1)dy – y√(y2 – 1)dx = 0

x√(x2 – 1)dy = y√(y2 – 1)dx

Thus, the statement (i) is true

Also, we can write Eq. (i) as 

Thus, the statement (ii) is false.

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