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WTW256: Lu 2.2: NON-HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS: Lecture Notes $4.51   Add to cart
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WTW256: Lu 2.2: NON-HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS: Lecture Notes
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  • Course
  • WTW 256 - Differential Equations
  • Institution
  • University Of Pretoria (UP)

Lecture notes were made while watching the recorded lectures assigned to watch. These notes include theory (theorems) and worked out examples from the lecturer. These specific notes cover Non-homogeneous linear differential equations, method of undetermined coefficients.

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Document information

  • July 11, 2022
  • 8
  • 2021/2022
  • Class notes
  • Ms l mostert
  • All classes

Subjects

  • wtw
  • wtw256
  • 256
  • non homogeneous
  • non homo
  • undetermined coefficients
  • method of undetermined coefficients

Written for

  • University of Pretoria (UP)
  • WTW 256 - Differential Equations
All documents for this subject (43)

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2. 2. Non -
linear Homo D. E.

Not equal
to taro
↳ where RHS is

Non homo PE 's with
-
constant coeff

'M 'm )
⑧
Any dn ly uqyliqoy -0
'

n -
1
. .
.




⑤ is the general solution of
@
L complimentary solution


⑧ is particular solution of the non hombf ④
-




a



A general solution • 1-
④ is
y= yciyp
( campy part)

IM-eth-od-ot-un-detirm-ine-dioei-f.it"
derivatives
- -
- -




and
-
- -




-
1. consider glx) ( RHS) to
guess a general form of yp
2. Then consider yc to check for duplication of terms

in yp

3 If NO DUPLICATIONS of terms in yp and
go
=
.




•

plug yp into DE ④ and compare coeff .

, Examples
1. Use method to solve :



2nd order
72g -3g guy
"
'
Y
.
-




with
27C
1. 1. gin)= @
N2
1. 2
gla)
=




91×1=9
"
1.3 and ya)=1 y
'



, (a) =4
"
In) :c
LU
g.
2 "
Trial :




µµ
1- 1
yo
'



.




-




2"
Yp A @
:

M 'T 2m -3
= 0


( Mt 3) ( m 1)
-
-0
'

NO duplication
m ,
, , m ,
,
, ,, a ]
g.f- ZAC
'"
ypl
=

-3 " a


¥
'
Cle i
Cz @
"
4Ae
"

yp
:




% Plug into Df :




Zyp 3yp=e2
" ' "
'
Yp
-




general solution
3AAe"=e2
" "

4AAe '^4☆e
"
"
-




Cle "nCze"uY5e
-3
y lm
-
_




22
4 4 -3 @
=
1
~

yc YP 5AAe =e
④ see that yp is the 5nA = I

solution that AA 45
only >
has value for the
,y}
a
.

'
coeff .
I 15cm

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