NCERT Class 12 · Ch 5 Exercise 5.7 · Q14
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.7 Question 14
If y=\(A e^{m x} + B e^{n x}\), show y″−(m+n)y′+mny=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″−(m+n)y′+mny=0
- First derivative: y′=\(A m e^{m x} + B n e^{n x}\).
- Second derivative: y″=\(A m^{2} e^{m x} + B n^{2} e^{n x}\).
- Substitution into the indicated left-hand combination and simplification gives \(0\).
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