NCERT Class 12 · Ch 9 Miscellaneous Exercise · Q9
NCERT Class 12 Maths · Chapter 9 Differential Equations · Miscellaneous Exercise Question 9
Solve (x−y)(dx+dy)=dx−dy, 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: x+y=log(x−y)−1 on the initial branch.
- Put t=x−y so dt=dx−dy. The equation gives d(x+y)=dt/t when t≠0.
- Thus x+y=log|x−y|+C. At (0,−1), t=1 and C=−1. The initial branch has x−y>0.
- Differentiate the resulting relation to recover the equation on intervals where the original expressions and the required slope are defined.
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