Question

If y = [x + √(x² - 1)]¹⁵ + [x - √(x² - 1)]¹⁵, then (x² - 1)d²y/dx² + x(dy/dx) is equal to 

(A) 225 y² 

(B) 224 y² 

(C) 125 y 

(D) 225 y

Answer 1

Answer is (D) 225 y

The given equation is

y = [x + √(x² - 1)]¹⁵ + [x - √(x² - 1)]¹⁵

Differentiating w.r.t. x, we get

Here, we have used the standard differentials

Differentiating w.r.t. x, we get