28. For each of the following equations, find the most general function N(x, y) so that the equation is exact. (a) [y cos (xy) + e*]dx + N(x, y) dy = 0 (b) (yey - 4x³y + 2) dx + N(x, y) dy = 0
28. For each of the following equations, find the most general function N(x, y) so that the equation is exact. (a) [y cos (xy) + e*]dx + N(x, y) dy = 0 (b) (yey - 4x³y + 2) dx + N(x, y) dy = 0
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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Question
question 28
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(a) [y cos (xy) + e*]dx + N(x, y) dy = 0
(b) (yey - 4x³y + 2) dx + N(x, y) dy = 0
(y² + 2xy) dx - x² dy = 0.
(a) Show that this equation is not exact.
(b) Show that multiplying both sides of the equation by
y2 yields a new equation that is exact.
(c) Use the solution of the resulting exact equation to
solve the original equation.
(d) Were any solutions lost in the process?
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Transcribed Image Text:near,
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27. For each of the following equations, find the most gen-
eral function M(x, y) so that the equation is exact.
28. For each of the following equations, find the most
general function N(x, y) so that the equation is exact.
#
3
29. Consider the equation
80
(a) M(x, y) dx + (sec²y = x/y) dy = 0
(b) M(x, y) dx +
F3
E
30. Consider the equation
D
(a) [y cos (xy) + e*]dx + N(x, y) dy = 0
(b) (yey - 4x³y + 2) dx + N(x, y) dy = 0
(y² + 2xy) dx - x² dy = 0.
(a) Show that this equation is not exact.
(b) Show that multiplying both sides of the equation by
y2 yields a new equation that is exact.
(c) Use the solution of the resulting exact equation to
solve the original equation.
(d) Were any solutions lost in the process?
$
4
(5r²y +6r³₂₂2 + 4 rv₂²) dr
888
(sin x cos y - xy - e) dy = 0
R
F
%
5
T
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6
MacBook Air
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8
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