NCERT Class 12 · Ch 9 Exercise 9.3 · Q3
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 3
Solve y′+y=1, y≠1.
💡 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=1+Ce^(−x), C≠0.
- Separate dy/(1−y)=dx. Integration gives −log|1−y|=x+C.
- Thus y=1+Ce^(−x), C≠0 under y≠1.
- Differentiate the resulting relation to recover the equation on intervals where the original expressions and the required slope are defined.
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All Questions in Differential Equations — Exercise 9.3
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