Solve the differential equation dy/dx = (1 + y²) / (1 + x²).

Solve the differential equation dy/dx = (1 + y²) / (1 + x²).

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

Answer: A) y − x = C(1 + xy)

Explanation: dy/(1+y²) = dx/(1+x²). Integrating: tan⁻¹y = tan⁻¹x + c. Let c = tan⁻¹C. Then tan⁻¹y − tan⁻¹x = tan⁻¹C → tan⁻¹[(y−x)/(1+xy)] = tan⁻¹C → (y−x)/(1+xy) = C.