Solution of the differential equation (x + y) dy − dx = 0 is:

Solution of the differential equation (x + y) dy − dx = 0 is:

• A. x + y + 1 = C eʸ
• B. x + y − 1 = C eʸ
• C. x − y + 1 = C eˣ
• D. x + y = C eˣ

Answer: A) x + y + 1 = C eʸ

Explanation: dx/dy = x + y → dx/dy − x = y. This is a linear DE in x. IF = e^(∫−1 dy) = e⁻ʸ. Solution: x(e⁻ʸ) = ∫y e⁻ʸ dy + C. Integrating by parts: −y e⁻ʸ − e⁻ʸ + c. Multiply by eʸ: x = −y − 1 + C eʸ, which is x + y + 1 = C eʸ.