NCERT Class 12 · Ch 9 Exercise 9.3 · Q2
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 2
Solve y′=√(4−y²), −2<y<2.
💡 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: sin⁻¹(y/2)=x+C; equivalently y=2sin(x+C) on branches −π/2<x+C<π/2.
- Separate dy/√(4−y²)=dx and integrate.
- The principal inverse yields sin⁻¹(y/2)=x+C. The branch restriction ensures cos(x+C)>0 so the derivative equals the nonnegative radical.
- The constant endpoint solutions y=±2 solve the equation if that domain is extended, but the stated open y-range excludes them.
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