NCERT Class 12 · Ch 9 Exercise 9.2 · Q10
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.2 Question 10
Verify y=\(\sqrt{a^{2} - x^{2}}\) solves x+yy′=0, −a<x<a, y≠0.
💡 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: Verified on the stated real domain.
- Differentiate the proposed function: y′=\(- \frac{x}{\sqrt{a^{2} - x^{2}}}\).
- Substitution into the equation leaves \(0\); hence it is satisfied. Require a>0 and −a<x<a.
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