NCERT Class 12 · Ch 9 Exercise 9.5 · Q11
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.5 Question 11
Solve x′+\(\frac{1}{y}\) 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 = \(\frac{3 C + y^{3}}{3 y}\), for y≠0; also retain the constant solution y=0 of the original differential form.
- Write x′ + \(\frac{1}{y}\) x = \(y\); work for y≠0; also retain the constant solution y=0 of the original differential form.
- An integrating factor is μ=\(y\), since μ′/μ=\(\frac{1}{y}\).
- Multiply through: d(μx)/dy = \(y^{2}\).
- Integrate the right side: \(\frac{y^{3}}{3}\). Thus μx=\(\frac{y^{3}}{3}\)+C.
- Therefore x = \(\frac{3 C + y^{3}}{3 y}\).
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