NCERT Class 12 · Ch 9 Exercise 9.3 · Q5
NCERT Class 12 Maths · Chapter 9 Differential Equations · Exercise 9.3 Question 5
Solve (eˣ+e^(−x))dy−(eˣ−e^(−x))dx=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: \(y - \log{\left(e^{x} + e^{- x} \right)}\) = C.
- Divide by eˣ+e^(−x)>0 to isolate y′.
- Its numerator is the derivative of its denominator. Integrating gives y=log(eˣ+e^(−x))+C.
- Differentiate the resulting relation to recover the equation on intervals where the original expressions and the required slope are defined.
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