NCERT Class 12 · Ch 9 Exercise 9.3 · Q9
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 9
Solve y′=sin⁻¹x.
💡 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: \(- x \operatorname{asin}{\left(x \right)} + y - \sqrt{1 - x^{2}}\) = C.
- Integrate by parts with u=sin⁻¹x and dv=dx.
- The remaining integral is ∫x/√(1−x²)dx=−√(1−x²), so y=x sin⁻¹x+√(1−x²)+C on −1<x<1.
- Differentiate the resulting relation to recover the equation on intervals where the original expressions and the required slope are defined.
Master Chapter 9: Differential Equations
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All Questions in Differential Equations — Exercise 9.3
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