Given the following differential equation [2xy + 6] dx + [x2 - 3y2] dy = 0 And that "F" is F = yx? + 6x + g (y) Find the equation that represents g(y). (A) 8 (y) = -y3 - 6y + C B 8(y) = -y3 + C © 8 (y) = - 3y3 + C %3D D 8 (y) - 3xy2 + C %3D (E) 8 (y) = 2xy + C F 8 (y) = x2 + C G 8 (y) = C

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...
Question

q7

Given the following differential equation
[2xy + 6] dx + [x2 – 3y2] dy = 0
And that "F" is
F = yx2 + 6x + 8 (y)
Find the equation that represents g(y).
A 8 (y) = -y3 - 6y + C
8 (y) = -y3 + C
C8 (y) = - 3y3 + C
D
8 (y) = - 3xy2 + C
(E
g (y) = 2xy + C
F
8 (y) = x2 + C
G
8 (y) = C
Transcribed Image Text:Given the following differential equation [2xy + 6] dx + [x2 – 3y2] dy = 0 And that "F" is F = yx2 + 6x + 8 (y) Find the equation that represents g(y). A 8 (y) = -y3 - 6y + C 8 (y) = -y3 + C C8 (y) = - 3y3 + C D 8 (y) = - 3xy2 + C (E g (y) = 2xy + C F 8 (y) = x2 + C G 8 (y) = C
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