​ If y = log(x – √(x^2 + 1)), show that (x^2 + 1)y2 + xy1 = 0 ​

Question

If y = log(x – \(\sqrt{x^2 + 1}\)), show that (x² + 1)y₂ + xy₁ = 0

Answer 1

2y₁ . y₂(1 + x²) + y₁²(2x) = 0 ÷ 2y₁ 

⇒ (1 + x²)y₂ + xy₁ = 0.