NCERT Class 12 · Ch 9 Exercise 9.5 · Q2
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.5 Question 2
Solve y′+\(3\) y=\(e^{- 2 x}\).
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: y = \(\left(C + e^{x}\right) e^{- 3 x}\), on intervals where the original equation is defined.
- Write y′ + \(3\) y = \(e^{- 2 x}\); work on intervals where the original equation is defined.
- An integrating factor is μ=\(e^{3 x}\), since μ′/μ=\(3\).
- Multiply through: d(μy)/dx = \(e^{x}\).
- Integrate the right side: \(e^{x}\). Thus μy=\(e^{x}\)+C.
- Therefore y = \(\left(C + e^{x}\right) e^{- 3 x}\).
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