NCERT Class 12 · Ch 9 Exercise 9.3 · Q18
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 18
The tangent slope is twice the slope from (−4,−3) to (x,y). Find the curve through (−2,1).
💡 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=(x+4)²−3, x>−4.
- The equation is y′=2(y+3)/(x+4).
- Separate and integrate: log|y+3|=2log|x+4|+C, so y+3=C(x+4)².
- The initial point gives 4=4C, hence C=1. The interval through the point has x>−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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