Determine whether the given differential equation is separable. dy = 5y² - 4y+1 dx Is the differential equation separable? dy OA. Yes, because = g(x)p(y) where g(x) = 5 and p(y) = y² - 4y + 1. dx dy OB. Yes, because = g(x)p(y) where g(x) = 1 and p(y) = 5y² - 4y + 1. dx dy O C. Yes, because = g(x)p(y) where g(x) = 1 and p(y) = 5y² - 4y. dx O D. No
Determine whether the given differential equation is separable. dy = 5y² - 4y+1 dx Is the differential equation separable? dy OA. Yes, because = g(x)p(y) where g(x) = 5 and p(y) = y² - 4y + 1. dx dy OB. Yes, because = g(x)p(y) where g(x) = 1 and p(y) = 5y² - 4y + 1. dx dy O C. Yes, because = g(x)p(y) where g(x) = 1 and p(y) = 5y² - 4y. dx O D. No
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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![### Determine Whether the Given Differential Equation is Separable
Given differential equation:
\[ \frac{dy}{dx} = 5y^2 - 4y + 1 \]
#### Is the differential equation separable?
___
- **A.** Yes; because \(\frac{dy}{dx} = g(x)p(y)\) where \(g(x) = 5\) and \(p(y) = y^2 - 4y + 1\).
- **B.** Yes; because \(\frac{dy}{dx} = g(x)p(y)\) where \(g(x) = 1\) and \(p(y) = 5y^2 - 4y + 1\).
- **C.** Yes; because \(\frac{dy}{dx} = g(x)p(y)\) where \(g(x) = 1\) and \(p(y) = 5y^2 - 4y\).
- **D.** No.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00114bb1-0365-4dfa-83cb-10b10c9a61b0%2Fb1e3d09f-9ace-44a4-bd1c-328ed8c37332%2F7a6q6p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determine Whether the Given Differential Equation is Separable
Given differential equation:
\[ \frac{dy}{dx} = 5y^2 - 4y + 1 \]
#### Is the differential equation separable?
___
- **A.** Yes; because \(\frac{dy}{dx} = g(x)p(y)\) where \(g(x) = 5\) and \(p(y) = y^2 - 4y + 1\).
- **B.** Yes; because \(\frac{dy}{dx} = g(x)p(y)\) where \(g(x) = 1\) and \(p(y) = 5y^2 - 4y + 1\).
- **C.** Yes; because \(\frac{dy}{dx} = g(x)p(y)\) where \(g(x) = 1\) and \(p(y) = 5y^2 - 4y\).
- **D.** No.
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