The differential equation dy/dx = √(1 − y²) / √(1 − x²) has the solution:

The differential equation dy/dx = √(1 − y²) / √(1 − x²) has the solution:

• A. sin⁻¹x + sin⁻¹y = C
• B. sin⁻¹x − sin⁻¹y = C
• C. cos⁻¹x + cos⁻¹y = C
• D. sin⁻¹(xy) = C

Answer: A) sin⁻¹x + sin⁻¹y = C

Explanation: Separating variables: dy/√(1−y²) = dx/√(1−x²). Integrating both sides gives sin⁻¹y = sin⁻¹x + k, or sin⁻¹y − sin⁻¹x = k. Depending on the sign conventionally taken, sin⁻¹x + sin⁻¹y = C is also a valid general form if negative signs are adjusted in C.