If y = e^(a sin⁻¹ x), then (1 − x²)y₂ − xy₁ equals:
If y = e^(a sin⁻¹ x), then (1 − x²)y₂ − xy₁ equals:
- A. a²y
- B. −a²y
- C. ay
- D. 0
Answer: A) a²y
Explanation: y₁ = e^(a sin⁻¹ x) × a/√(1−x²) = a y/√(1−x²). So √(1−x²) y₁ = a y. Squaring: (1−x²)y₁² = a² y². Differentiating: −2x y₁² + 2(1−x²)y₁ y₂ = 2a² y y₁. Divide by 2y₁: −x y₁ + (1−x²)y₂ = a² y.
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