WTW256: LU 2.1: SECOND AND HIGHER ORDER HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS Lecture notes
2 views 0 purchase
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.
an Ix ) Yh i
any Ln )Y
"^
} .
.
.iq , Cody 'eqoxy=gC c) >
y(xo)=yo- Not power to
but order of derivative
④ ✗a) =
y, -
1) ( xo ) Yh -1
ya :
-
Theorem 4.1.1 .
The IVD ⑦ solution yl ≥) on an
has a unique
interval 1 it the functions 9h / 9h I -
. . .
go
,
and g 2 and
are continuous on the interval
dhlx ) ¥0 for d 11 kt 1
DE it
Homogeneous gl a) a
=
↳ not like previous homo this is d HIGHER
ORDER HOMO ! !
,
⑤ any.hn .
.
.to ,y'yqoy=o
Theorem 4.1.2 .
If y , , yz . .
.yn are solutions of ② on an interval
2 , any linear combination of the solutions
GY It
CZY 24
=
y . . .
4
Cnyh
will also be a solution oh I CCER ,n=1, 2
,
. -
yn)
, linearly dependent functions
it constants 4,4 , Cs ,
. . .
,Cn , not all equal to Zero
,
can be found such that
Cifl Y Czfzt . . -
t Cnfn =
0
linearly dependent functions
If C , fly Czfzt Cnfn -0 implies that
'
. . -
t
4=02 =
.
. .
= Ch =
0
G)121 Czk 4 =
0
↓ ↓
positive hrs
zero if 4 :( 2=0
can
only be
i.
=
linearly independent
" 2" 0
☐ e Cz @
=
n
ex ≠ cel
"
↓ ↓ Cmu / tiple)
always positive .
?
Wronski ah of functions
findep
dep ?
criteria hest
•
mm
linearly Ep it W{ fi.fr ,
. . _
fn } =/ 0 for
all 71 C- 1
Fundamental set
solutions
set of linearly indep
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller lexisparks. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $4.56. You're not tied to anything after your purchase.