NCERT Class 12 · Ch 9 Miscellaneous Exercise · Q12
NCERT Class 12 Maths · Chapter 9 Differential Equations · Miscellaneous Exercise Question 12
Solve (x+1)y′=2e^(−y)−1 with y(0)=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: \(\log{\left(\frac{2 x + 1}{x + 1} \right)}\), x>−1/2.
- Let z=eʸ>0. Multiplying the equation by eʸ gives (x+1)z′+z=2.
- The left side is [(x+1)z]′, so (x+1)eʸ=2x+C.
- At (0,0), C=1, giving y=log[(2x+1)/(x+1)]. The maximal initial interval is x>−1/2.
- Differentiate the resulting relation to recover the equation on intervals where the original expressions and the required slope are defined.
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