NCERT Class 12 · Ch 9 Exercise 9.3 · Q6
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 6
Solve y′=(1+x²)(1+y²).
💡 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: \(- \frac{x^{3}}{3} - x + \operatorname{atan}{\left(y \right)}\) = C.
- Separate dy/(1+y²)=(1+x²)dx.
- Integrate to obtain tan⁻¹y=x+x³/3+C; an explicit tangent form is valid on intervals avoiding its poles.
- Differentiate the resulting relation to recover the equation on intervals where the original expressions and the required slope are defined.
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All Questions in Differential Equations — Exercise 9.3
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