NCERT Class 12 · Ch 9 Miscellaneous Exercise · Q6
NCERT Class 12 Maths · Chapter 9 Differential Equations · Miscellaneous Exercise Question 6
Find the curve through (0,π/4) for sin x cos y dx+cos x sin y dy=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: cos x cos y=1/√2, on the branch through (0,π/4).
- The left side is −d(cos x cos y). Thus cos x cos y=C.
- The initial point gives C=1/√2. Choose the branch containing y=π/4.
- Differentiate the resulting relation to recover the equation on intervals where the original expressions and the required slope are defined.
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