acdfjhfdcdj. THIS IS ABOUT EXACT DIFFERENTIAL EQUATIONS SHOW COMPLETE SOLUTIONS. JDFEHFEDHSHFSHC

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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acdfjhfdcdj. THIS IS ABOUT EXACT DIFFERENTIAL EQUATIONS SHOW COMPLETE SOLUTIONS. JDFEHFEDHSHFSHC

f(y) = sin y + c
From U(x, y) = yx²+f (y)
U(x, y) = x³y + sin y + c
x'y + sin y = c
or
Check:
dU = o
d(x*y + sin y) = o
y d(x²) + x² d(y) + d(sin y) = o
y(2x)dx + x² dy + cos y dy = o
dx + (x² + cos y) dy = o
2xy
%3D
dy _x- усosx
sin x+y
2.
dx
Transcribed Image Text:f(y) = sin y + c From U(x, y) = yx²+f (y) U(x, y) = x³y + sin y + c x'y + sin y = c or Check: dU = o d(x*y + sin y) = o y d(x²) + x² d(y) + d(sin y) = o y(2x)dx + x² dy + cos y dy = o dx + (x² + cos y) dy = o 2xy %3D dy _x- усosx sin x+y 2. dx
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