d) dª y dx4 +81y = 0
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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Question
D
![# Solving Differential Equations: General Solutions
Explore the following differential equations and find their general solutions.
### Equations
#### 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)
\[
\frac{d^6 y}{dx^6} + 8 \frac{d^4 y}{dx^4} + 16 \frac{d^2 y}{dx^2} y = 0
\]
### Instructions
To solve these differential equations, use techniques such as characteristic equations, undetermined coefficients, or variation of parameters. Each equation represents a different level and type of derivative, challenging your understanding and analysis of differential equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d410cd6-8fc6-4d13-8ff0-7a43ba3056bc%2Ffada4419-8349-47a9-b322-2079ddb44dfb%2Fjdg8rt8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Solving Differential Equations: General Solutions
Explore the following differential equations and find their general solutions.
### Equations
#### 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)
\[
\frac{d^6 y}{dx^6} + 8 \frac{d^4 y}{dx^4} + 16 \frac{d^2 y}{dx^2} y = 0
\]
### Instructions
To solve these differential equations, use techniques such as characteristic equations, undetermined coefficients, or variation of parameters. Each equation represents a different level and type of derivative, challenging your understanding and analysis of differential equations.
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