If y = (tan –1 x) 2 , show that (x 2 + 1) 2 y 2 + 2x (x 2 + 1) y 1 = 2

Question

Philoid · Accepted Answer

: It is given that

y = (tan^–1 x)²

On differentiating we get,

Again differentiating, we get,

So, (1+x²)²y₂ + 2x(1+x²)y₁ = 2

where,

Hence Proved