If y = {log (x + √x^2 + 1)^2, show that (1 + x^2) d^2y/dx^2+x dy/dx = 2.

Question

If y = {log (x + √x² + 1)², 

show that (1 + x²) \(\frac{d^2y}{dx^2}+x\frac{dy}{dx}\)= 2.

Answer 1

Formula: –

Using formual(iii) 

\(\Rightarrow (1+x^2)y_2+xy_1=2\)

Hence proved