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Determine whether the statement is true or false. True False The equation y' = 4y - 2x + 8xy - 1 is separable.

Determine whether the statement is true or false. True False The equation y' = 4y - 2x + 8xy - 1 is separable.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Determine Whether the Statement is True or False Consider the following statement and determine if it is true or false: **Statement:** "The equation \( y' = 4y - 2x + 8xy - 1 \) is separable." **Options:** - True - False In a separable differential equation, it is possible to separate the variables \( x \) and \( y \) on opposite sides of the equation. This means the equation can be written in the form: \[ g(y) \, dy = h(x) \, dx \] Carefully analyze the given equation to see if it can be rewritten in such a form. Select "True" if it can be separated or "False" if it cannot. **Note:** There are no graphs or diagrams associated with this content.
Transcribed Image Text:### Determine Whether the Statement is True or False Consider the following statement and determine if it is true or false: **Statement:** "The equation \( y' = 4y - 2x + 8xy - 1 \) is separable." **Options:** - True - False In a separable differential equation, it is possible to separate the variables \( x \) and \( y \) on opposite sides of the equation. This means the equation can be written in the form: \[ g(y) \, dy = h(x) \, dx \] Carefully analyze the given equation to see if it can be rewritten in such a form. Select "True" if it can be separated or "False" if it cannot. **Note:** There are no graphs or diagrams associated with this content.
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