Question

If y = tan^–1x, prove that (1 + x²)y² + 2xy₁ = 0

Answer 1

Given y = tan^–1x

⇒ dy/dx = 1/(1 + x²)

⇒ (1 + x²)(dy/dx)  = 1

⇒ (1 + x²)(d²y/dx²) + 2x(dy/dx) = 0

⇒ (1 + x²)y₂ + 2xy₁ = 0