What is the order of the set of differential equations shown below? dy (t) +y(t)=2x(t) dt dx (t) d?y(t) +x(t)= dt dt?
What is the order of the set of differential equations shown below? dy (t) +y(t)=2x(t) dt dx (t) d?y(t) +x(t)= dt dt?
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 1:**
*What is the order of the differential equations shown below?*
\[ x^2 \frac{d\theta(x)}{dx} + 2\theta(x) + \frac{d^3\theta(x)}{dx^3} = x^4. \]
Options:
- ○ 4
- ○ 2
- ● 3
- ○ 1
**Explanation:**
The highest derivative in this equation is \(\frac{d^3\theta(x)}{dx^3}\), which is a third derivative. Therefore, the order of the differential equation is **3**.
---
**Question 2:**
*What is the order of the set of differential equations shown below?*
\[ \frac{dy(t)}{dt} + y(t) = 2x(t) \]
\[ \frac{dx(t)}{dt} + x(t) = \frac{d^2y(t)}{dt^2} \]
Options:
- ○ 4
- ○ 3
- ○ 1
- ● 2
**Explanation:**
In the given set, the highest derivative is \(\frac{d^2y(t)}{dt^2}\), which is a second derivative. Hence, the order of the set of differential equations is **2**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2032bc4f-d7c2-4a7d-a3a7-5951ded4fcfd%2F1845a67a-4d18-4491-974c-147c9d5f703b%2F830aabn_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 1:**
*What is the order of the differential equations shown below?*
\[ x^2 \frac{d\theta(x)}{dx} + 2\theta(x) + \frac{d^3\theta(x)}{dx^3} = x^4. \]
Options:
- ○ 4
- ○ 2
- ● 3
- ○ 1
**Explanation:**
The highest derivative in this equation is \(\frac{d^3\theta(x)}{dx^3}\), which is a third derivative. Therefore, the order of the differential equation is **3**.
---
**Question 2:**
*What is the order of the set of differential equations shown below?*
\[ \frac{dy(t)}{dt} + y(t) = 2x(t) \]
\[ \frac{dx(t)}{dt} + x(t) = \frac{d^2y(t)}{dt^2} \]
Options:
- ○ 4
- ○ 3
- ○ 1
- ● 2
**Explanation:**
In the given set, the highest derivative is \(\frac{d^2y(t)}{dt^2}\), which is a second derivative. Hence, the order of the set of differential equations is **2**.
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