NCERT Class 12 · Ch 9 Exercise 9.5 · Q19
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.5 Question 19
Find an integrating factor for (1−y²)dx/dy+yx=ay, −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: D: 1/√(1−y²).
- Normalize: dx/dy+[y/(1−y²)]x=ay/(1−y²).
- ∫y/(1−y²)dy=−(1/2)log(1−y²); exponentiation gives 1/√(1−y²).
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