NCERT Class 12 · Ch 9 Exercise 9.5 · Q10
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.5 Question 10
Solve x′+\(-1\) x=\(y\).
💡 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: x = \(C e^{y} - y - 1\), on intervals where the original equation is defined.
- Write x′ + \(-1\) x = \(y\); work on intervals where the original equation is defined.
- An integrating factor is μ=\(e^{- y}\), since μ′/μ=\(-1\).
- Multiply through: d(μx)/dy = \(y e^{- y}\).
- Integrate the right side: \(\left(- y - 1\right) e^{- y}\). Thus μx=\(\left(- y - 1\right) e^{- y}\)+C.
- Therefore x = \(C e^{y} - y - 1\).
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