NCERT Class 12 · Ch 9 Exercise 9.5 · Q12
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.5 Question 12
Solve x′+\(- \frac{1}{y}\) x=\(3 y\).
💡 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 = \(y \left(C + 3 y\right)\), for y>0.
- Write x′ + \(- \frac{1}{y}\) x = \(3 y\); work for y>0.
- An integrating factor is μ=\(\frac{1}{y}\), since μ′/μ=\(- \frac{1}{y}\).
- Multiply through: d(μx)/dy = \(3\).
- Integrate the right side: \(3 y\). Thus μx=\(3 y\)+C.
- Therefore x = \(y \left(C + 3 y\right)\).
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