The general solution of the differential equation dy/dx + y = e⁻ˣ is:

The general solution of the differential equation dy/dx + y = e⁻ˣ is:

• A. y = (x + C)eˣ
• B. y = (x + C)e⁻ˣ
• C. y = x e⁻ˣ + C
• D. y = x eˣ + C

Answer: B) y = (x + C)e⁻ˣ

Explanation: P = 1, IF = e^(∫1 dx) = eˣ. Solution is y(IF) = ∫(Q × IF)dx + C. y(eˣ) = ∫(e⁻ˣ × eˣ)dx + C = ∫1 dx + C = x + C. Therefore, y = (x + C)e⁻ˣ.