NCERT Class 12 · Ch 9 Exercise 9.3 · Q14
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 14
Solve y′=y tan x, y(0)=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: y=sec x, −π/2<x<π/2.
- Separate dy/y=tan x dx; integrating gives y=C sec x.
- At x=0, y=1 gives C=1. The initial-value interval is (−π/2,π/2).
- Differentiate the resulting relation to recover the equation on intervals where the original expressions and the required slope are defined.
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