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d) da y dx4 +81y = 0

d) da y dx4 +81y = 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Solve the equation by finding a general solution.** a) \(\frac{d^3 y}{dx^3} - 3 \frac{d^2 y}{dx^2} + 3 \frac{dy}{dx} - y = 0\) b) \(\frac{d^3 y}{dx^3} - 3 \frac{d^2 y}{dx^2} + \frac{dy}{dx} - 3y = 0\) c) \(\frac{d^3 y}{dx^3} + 2 \frac{d^2 y}{dx^2} + 4 \frac{dy}{dx} = 0\) d) \(\frac{d^4 y}{dx^4} + 81y = 0\) e) \(\frac{d^5 y}{dx^5} - \frac{d^4 y}{dx^4} - 16 \frac{dy}{dx} + 16 = 0\) f) \(\frac{d^4 y}{dx^4} + 2 \frac{d^2 y}{dx^2} + y = 0\) g) \(\frac{d^6 y}{dx^6} + 8 \frac{d^4 y}{dx^4} + 16 \frac{d^2 y}{dx^2} y = 0\)
Transcribed Image Text:**Solve the equation by finding a general solution.** a) \(\frac{d^3 y}{dx^3} - 3 \frac{d^2 y}{dx^2} + 3 \frac{dy}{dx} - y = 0\) b) \(\frac{d^3 y}{dx^3} - 3 \frac{d^2 y}{dx^2} + \frac{dy}{dx} - 3y = 0\) c) \(\frac{d^3 y}{dx^3} + 2 \frac{d^2 y}{dx^2} + 4 \frac{dy}{dx} = 0\) d) \(\frac{d^4 y}{dx^4} + 81y = 0\) e) \(\frac{d^5 y}{dx^5} - \frac{d^4 y}{dx^4} - 16 \frac{dy}{dx} + 16 = 0\) f) \(\frac{d^4 y}{dx^4} + 2 \frac{d^2 y}{dx^2} + y = 0\) g) \(\frac{d^6 y}{dx^6} + 8 \frac{d^4 y}{dx^4} + 16 \frac{d^2 y}{dx^2} y = 0\)
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