Find the differential equation by eliminating arbitrary constants from the relation \(y=Ae^{3x}+Be^{-3x}\).
Q.3 (A) (iii) Find the differential equation by eliminating arbitrary constants from the relation \(y=Ae^{3x}+Be^{-3x}\).
1 answer
Best answer
Answer: \(\frac{d^2y}{dx^2}-9y=0\)
\(y=Ae^{3x}+Be^{-3x}\) ... (1)
\(\frac{dy}{dx}=3Ae^{3x}-3Be^{-3x}\)
\(\frac{d^2y}{dx^2}=9Ae^{3x}+9Be^{-3x}=9y\) by (1).
Hence the required differential equation is \(\frac{d^2y}{dx^2}-9y=0\).
Doubtly AI
· 28 Oct 2026
AI-verified · Oct 2026
Report
Was this answer helpful?
Thanks for the feedback.
Sign up free to save answers and ask your own doubts
Your answer
Log in or create a free account to answer this question.