NCERT Class 12 · Ch 9 Exercise 9.3 · Q16
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 16
Solve xy y′=(x+2)(y+2), passing through (1,−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−2log|y+2|=x+2log|x|−2 (initial branch through (1,−1)).
- Separate y/(y+2)dy=(x+2)/x dx.
- Integrate y−2log|y+2|=x+2log|x|+C. At (1,−1), C=−2.
- The branch through the initial point lies in x>0, −2<y<0 until its finite-slope description fails.
- Differentiate the resulting relation to recover the equation on intervals where the original expressions and the required slope are defined.
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