dy + (y – 1). + 4y – 1)5 COS I dr
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
Determine the order of the given
![Certainly! Below is the transcription of the provided image for an educational website.
---
### Differential Equation
The differential equation representation in the image is as follows:
\[
x^2 \frac{d^4y}{dx^4} + (y - 1) \frac{dy}{dx} + 4y = \cos x
\]
#### Explanation:
This is a higher-order differential equation where:
- \( x \) is the independent variable.
- \( y \) is the dependent variable.
- \(\frac{d^4y}{dx^4}\) denotes the fourth derivative of \( y \) with respect to \( x \).
- \(\frac{dy}{dx}\) denotes the first derivative of \( y \) with respect to \( x \).
- \( \cos x \) is the cosine function of \( x \).
The equation combines various orders of derivatives of \( y \) along with the trigonometric function \( \cos x \). This type of equation may arise in advanced applications such as physics or engineering, particularly when dealing with systems involving vibrations or oscillations.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc262d38-8642-4292-8f86-e10c24c29ddb%2F9910faa8-9ecc-4e07-ad1f-d171f7e4559c%2F99ewc8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Below is the transcription of the provided image for an educational website.
---
### Differential Equation
The differential equation representation in the image is as follows:
\[
x^2 \frac{d^4y}{dx^4} + (y - 1) \frac{dy}{dx} + 4y = \cos x
\]
#### Explanation:
This is a higher-order differential equation where:
- \( x \) is the independent variable.
- \( y \) is the dependent variable.
- \(\frac{d^4y}{dx^4}\) denotes the fourth derivative of \( y \) with respect to \( x \).
- \(\frac{dy}{dx}\) denotes the first derivative of \( y \) with respect to \( x \).
- \( \cos x \) is the cosine function of \( x \).
The equation combines various orders of derivatives of \( y \) along with the trigonometric function \( \cos x \). This type of equation may arise in advanced applications such as physics or engineering, particularly when dealing with systems involving vibrations or oscillations.
---
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