If y = (e^{\tan^{- 1}x}) then which one is true – | MATH - DIFFERENTIATION BY SUBSTITUTION, HIGHER ORDER DERIVATIVES | SolveeIt

If y = $e^{\tan^{- 1}x}$ then which one is true –

(1 +x²) y₂ – (2x – 1) y₁ = 0

(1 + x²) y₂ + (2x +1) y₁ = 0

(1 + x²)y₂ + (2x – 1) y₁ + y = 0

(1 + x²) y₂ + (2x – 1) y₁ = 0

Answer

(1 + x²) y₂ + (2x – 1) y₁ = 0

Explanation

y = $e^{\tan^{- 1}x}$ ⇒ y₁ = $e^{\tan^{- 1}x}$ $\frac{1}{1 + x^{2}}$

⇒ (1 +x²)y₁ = $e^{\tan^{- 1}x}$ = y

Now again differentiate w.r.t. x.

Question: If y = \(e^{\tan^{- 1}x}\) then which one is true –...