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Class 12 Differential Equations · Conceptual Answer1 Marksfirst_order_differential_equations

Class 12 Maths · Differential Equations · Conceptual Answer #90

Is y = e^(−x)(x + a) a solution of y′ + y = e^(−x), for constant a?

✅ Step-by-Step Solution

Final Answer: Yes, for every real a.
  1. Differentiate: y′ = e^(−x)(1 − x − a). Adding y gives e^(−x).
  2. Yes, for every real a.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Differentiate: y′ = e^(−x)(1 − x − a). Adding y gives e^(−x).
  • [0.5 marks] Yes, for every real a.

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