chapter 21 exact differential equation chapter 2 exact differential equation
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Chapter 2 1
Exac
t D
iffer
entia
l Equ
ation
C
hapt
er 2 Exact Differential Equation
Chapter 2 2
Exac
t D
iffer
entia
l Equ
ation
C
hapt
er 2
Chapter 2 3
Exac
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iffer
entia
l Equ
ation
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er 2
Exactness Test
Chapter 2 4
Exac
t D
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entia
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ation
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er 2
STEP:1
STEP:2
Chapter 2 5
Exac
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entia
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ation
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STEP:3
Find k(y)
STEP:4
STEP:5
STEP:6
Chapter 2 6
Exac
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ation
C
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Chapter 2 7
Exac
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ation
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Chapter 2 8
Exac
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N , DE is not exact.
x
M
y
Making Exact
IF
Chapter 2 9
Exac
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Multiply by F(x) or G(y)
Chapter 2 10
To m
ake
Exac
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entia
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ation
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hapt
er 2
Chapter 2 11
To m
ake
Exac
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ation
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Chapter 2 12
To m
ake
Exac
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ation
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Chapter 2 13
To m
ake
Exac
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ation
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2 2(3 ) ( ) 0dy
xy y x xydx
Exercise:Solve the differential equation by making it exact
cyxyx 223
2
1
Solution is
Integrating factor is f(x) = x
14Chapter 2
To m
ake
Exac
t D
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entia
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ation
C
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er 2
Exercise:
Integrating factor is
Solution is
2( )g y y
22xycy
C = 5
2 2 5x y y
Chapter 2 15
Firs
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First Order Linear Differential Equations
Chapter 2 16
Firs
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Cha
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2 Method
Chapter 2 17
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Chapter 2 18
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Chapter 2 19
Firs
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Exercise:
Chapter 2 20
Firs
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Chapter 2 21
Firs
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