NCERT Class 12 · Ch 9 Exercise 9.3 · Q17
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 17
Find the curve through (0,−2) where y times the tangent slope equals x.
💡 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=−√(x²+4).
- The equation is yy′=x, so integrating y dy=x dx gives y²−x²=C.
- At (0,−2), C=4. Choose the negative branch: y=−√(x²+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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