The differential equation bx [a y sin (5x) + 2e'* cos(4y) +mx²] dx + [cos(cx) + 2eb* sin(4y)] dy = 0 is exact for a = -5, b = −4, c = 5, m any real is exact for a = −5, b = 5, c = -4, m any real is exact for b = -4, c = 5 and any reals a, m is exact for a = −5, b = −4, c = 5, m = 0 only is never exact The differential equation x-4 y² dx + (y² + x¯³ y² + 6) dy = 0 is non exact and has integrating factor μ(y) non exact and has integrating factor μ(x) non exact and has integrating factor μ(y) non exact and has integrating factor μ(y) = = = уг езу x2 е x -2 -3 y е = y³ e² y exact non exact and has integrating factor μ(x) =x-2-3x

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
The differential equation
bx
[a y sin (5x) + 2e'* cos(4y) +mx²] dx + [cos(cx) + 2eb* sin(4y)] dy = 0
is exact for a =
-5, b
=
−4, c = 5, m any real
is exact for a = −5, b = 5, c = -4, m any real
is exact for b = -4, c = 5 and any reals a, m
is exact for a = −5, b
=
−4, c = 5, m = 0 only
is never exact
Transcribed Image Text:The differential equation bx [a y sin (5x) + 2e'* cos(4y) +mx²] dx + [cos(cx) + 2eb* sin(4y)] dy = 0 is exact for a = -5, b = −4, c = 5, m any real is exact for a = −5, b = 5, c = -4, m any real is exact for b = -4, c = 5 and any reals a, m is exact for a = −5, b = −4, c = 5, m = 0 only is never exact
The differential equation x-4 y² dx + (y² + x¯³ y² + 6) dy = 0 is
non exact and has integrating factor μ(y)
non exact and has integrating factor μ(x)
non exact and has integrating factor μ(y)
non exact and has integrating factor μ(y)
=
=
=
уг езу
x2
е
x
-2
-3 y
е
=
y³ e² y
exact
non exact and has integrating factor μ(x)
=x-2-3x
Transcribed Image Text:The differential equation x-4 y² dx + (y² + x¯³ y² + 6) dy = 0 is non exact and has integrating factor μ(y) non exact and has integrating factor μ(x) non exact and has integrating factor μ(y) non exact and has integrating factor μ(y) = = = уг езу x2 е x -2 -3 y е = y³ e² y exact non exact and has integrating factor μ(x) =x-2-3x
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