If y = (tan⁻¹ x)², then (1 + x²)² y₂ + 2x(1 + x²)y₁ is equal to:
If y = (tan⁻¹ x)², then (1 + x²)² y₂ + 2x(1 + x²)y₁ is equal to:
- A. 2
- B. 0
- C. 1
- D. 4y
Answer: A) 2
Explanation: y₁ = 2 tan⁻¹ x / (1+x²). So (1+x²)y₁ = 2 tan⁻¹ x. Differentiating: 2x y₁ + (1+x²)y₂ = 2/(1+x²). Multiply by (1+x²): 2x(1+x²)y₁ + (1+x²)² y₂ = 2.
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