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The solution of the differential equation dy/dx + (1 + y²)/sqrt(1 - x²) = 0 is:
- tan⁻¹ y + sin⁻¹ x = c
- tan⁻¹ x + sin⁻¹ y = c
- tan⁻¹ y * sin⁻¹ x = c
- cot⁻¹(1/y) + cos⁻¹ sqrt(1 - x²) = c
Correct answer: tan⁻¹ y + sin⁻¹ x = c
Solution
Separating variables gives dy/(1+y²) = -dx/sqrt(1-x²); integrating both sides yields tan⁻¹ y + sin⁻¹ x = c.
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