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For each of the following differential equations, determine whether it is an exact equation or not. If it is, calculate a general solution; if it is not, state that the method of exact equations does not apply. (2+7² - y²) dx + (1²-2 (y² - 2xy + 24-²y) d 3 b. (2xy - 3y) dx + (−6x+3y + 2x²) dy = 0 a. dy = 0 When solved for the derivative, assuming y0, each of the equations a and b is equivalent to the following first-order ODE: dy dx -2xy + 3y 2x² - 6x + 3y Nonetheless, applying the method of exact equations yields different results!

For each of the following differential equations, determine whether it is an exact equation or not. If it is, calculate a general solution; if it is not, state that the method of exact equations does not apply. (2+7² - y²) dx + (1²-2 (y² - 2xy + 24-²y) d 3 b. (2xy - 3y) dx + (−6x+3y + 2x²) dy = 0 a. dy = 0 When solved for the derivative, assuming y0, each of the equations a and b is equivalent to the following first-order ODE: dy dx -2xy + 3y 2x² - 6x + 3y Nonetheless, applying the method of exact equations yields different results!

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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For each of the following differential equations, determine whether it is an exact equation or not. If it is, calculate a general solution; if it is not, state that the method of exact equations does not apply. a. (2x² - y²) dx + (1² - 2xy + ²x²) dy: dy = 0 3 3 b. (2xy − 3y) dx + (−6x + 3y + 2x²) dy = 0 - When solved for the derivative dy, assuming y ‡ 0, each of the equations a and b is equivalent to the following first-order ODE: dy -2xy + 3y dx 2x² - 6x + 3y Nonetheless, applying the method of exact equations yields different results! =
Transcribed Image Text:For each of the following differential equations, determine whether it is an exact equation or not. If it is, calculate a general solution; if it is not, state that the method of exact equations does not apply. a. (2x² - y²) dx + (1² - 2xy + ²x²) dy: dy = 0 3 3 b. (2xy − 3y) dx + (−6x + 3y + 2x²) dy = 0 - When solved for the derivative dy, assuming y ‡ 0, each of the equations a and b is equivalent to the following first-order ODE: dy -2xy + 3y dx 2x² - 6x + 3y Nonetheless, applying the method of exact equations yields different results! =
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