Find the function M(x, y) such that M (x, 0) = eª and the differential equation M(x, y) dx + (sin x cos y - xy - e-)dy = 0 is exact. O sina sin y + y² + ex cos x sin y + y² + e- 2 cos x sin y - y² + e-ª cos a sin y-y² + é sin x sin y y² +e=² x

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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Find the function M(x, y) such that M (x, 0) = eª and the differential equation
M(x, y) dx + (sin x cos y - xy - e-)dy = 0 is exact.
O sina sin y + y² + ex
cos x sin y + y² + e-
2
cos x sin y - y² + e-ª
cos a sin y-y² + é
sin x sin y
y² +e=²
x
Transcribed Image Text:Find the function M(x, y) such that M (x, 0) = eª and the differential equation M(x, y) dx + (sin x cos y - xy - e-)dy = 0 is exact. O sina sin y + y² + ex cos x sin y + y² + e- 2 cos x sin y - y² + e-ª cos a sin y-y² + é sin x sin y y² +e=² x
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