• Wrong document? Swap it for free
  • Written by students who passed
  • Immediately available after payment
  • Read online or as PDF
Sell
Where do you study
Your language
Document preview thumbnail
Preview 3 out of 24 pages
Interview

Physics and maths notes available

Document preview thumbnail
Preview 3 out of 24 pages

Please subscribe my account for More notes

Content preview

7-.E><a\fc§_5@




,
’ g — W




l.?£2!§‘J£!'¥£.!%sI 9% M1@@w»~k?@
'\/\
L
I3'
4 "-"<1 ---1' " -‘ ' - --~'- -1 .- ‘ -~ .-.. ::. u .. .' - -< r.>m r _+..,~,,,\_g,~.‘ 51:.-.,~,-...-4..,_..._,-,.,_ ,,_,,,..>._
Q Q Q. ,,_ /‘ {V-5




F
. €
I . :,.> . ' . " - :'
‘ ‘ mi 5 . 4




‘,...\..‘-'-.
Y~.;:.-.5 3:3 39- ‘T-... . .
,

7 ".'§¢,--__§_¢__:.)¢.pv,.-,1 .‘
.' I »;., . ; . ..~->_-'._'.' -
.
w

x‘ I. .
i
i ' ', -



-'~
- » - Y




‘ A i- ~3=*;==4;~. Y . 1' 1




' .; ‘I352-;;;»L~_’ .;;1.S"=[=: , V 1 ¢ ‘ v I

.
‘ . ‘ V ‘ . n I > %
'

.
g I
D _>
;Y-'1‘ 5v",',A|.'-1<'.~-1'-6"
:Jf.:14_-._
- '
- Q I D - ‘|
/4 . .1-:1-:-<,w .»=~:w;' '--.-. . V _ .
. . Y -


' J
.~ ,

'.'.-->}~>¢g\_-" ",~\-. _\ 1- >
.


_
iv

I EB E .


. - L
1 _ ...
§.f>1-.§;'.»‘
...,._,_ .
. ’-‘ _ ~ ~
-


I . ,_‘,-.-7
l
M
.= = »v;;.-.1--;;:_; ‘
._~
" » .-
V »_,.A 4-z. - .--
I




l~ ‘ I
.

I
| 1 W°?€AE‘*@EE%€
' Q .
- '3', --. v ‘ 1; ‘-2- 1. ; ':-,.-.'- 1.1 -_- a -:;\‘.‘,v|»-.\. ; '~e. .,, ~_, .¢.._»4 "\l<,1b§_\"1\1\|‘L-vi4{ITY“'I“»\'1‘§'l4A||.'fP‘“',Vg ,|‘4y|wg> -.~. W .1:¢_;;\,¢,,”;=;-:;;,~,;m¢,y.-51
I


i




Non Linear Diff. Eq-" 50j_?0Ifder one Y




Am eq-L which is mat‘ linear, is colleql Norw-Linear} (See ch-‘10)'

Cor‘w5ic>le»-‘the non-'lineor diff» §eq- ffsb order‘ ’


0
2




_ - ~ 1
.~\

f( 15.91’ I’ §
1




or = 0 l Z ~ . I , A



I I



.

5


1
TF1gs,'we usually , ‘raprasents NQm__[_i,.r\e;Qr ‘cliff e.q- -of U13
first Or‘>dE.r by }(X'9'p) = O’ whe_.'_Q' P__=_Q_L1~__l__

oil .’
‘z
J
We shall discuss the fouhr Le_¢A}-‘ml-ques to 5O\V‘e_ the eq..J(1’@#§),=o
v




‘.1


'5
é .




S0|vobl<=_ for P ‘




l

Solvobla 3

.\{
0

./ H|
|

\ ‘3 '
\




Solvable ‘for ')(

ClOir"OuL7s QC]-' '

I
$




l?
"?1‘£i#;i?)L+(*“n"a”~n>%@‘-“=>‘v” ’


la” L
~




.\ '2, 0|,’/0&0» _3___ ___a_l_7_g_ éb L’
MW
|




@>‘v+v "><»~,><w>=>m?)
1




i-»(j"--Q<:9_.v"_‘<\j) =xawU§i 5). "“ £51.“

I)‘/ULCZ-bi L’ X,‘ - 3-» gi.::7 V2’ '\,., ' <'

“"3 H»
V




A J 3 3)-W 3 °%‘i*"‘:K ‘?if’"Y~ 2:‘

, B;
¢



§-11'
. 85 '
\f.;
1
P §@lwabe mt. P ~
' -, , ,. .1,-,_-§_g~j_q\.e7'_ .¢,_¢.,-,-*,- .~ -




.1.‘




3i|
"me diff. q. £1 3'9) = £5‘ 50; O be _,olvable. for P
}

if il; can be 'veoluc;eoL irwto 1-irwear factors-

: ' I ‘ I




r

.




; 0.
1 -




Examgpe 1,531+ W- Qty '



501:” 2
XP-E] 1
2.
-0- 7(.?"EJ = O

=v (1P+,9)-(v¢P—a) + (><P—93 '= O

=w (1P_—3)[1_£P+3+\} =0
' =v vLP-3 o or xP+g,+| _= o-
-.1



e
I ’ xP—~'j ' 7 1?+~_1+\.=Q
4?
J1 IT!‘ 1_ =..
2.. ,_'% d
at--i -:_'. H ‘
Q d~
X -Ely-gk =
.., I



c>k9=_g_;
WF
3


'.




‘
1.
I
I ‘zv
I
=>
. ,'
§i=<>_L£
I
H


"L
I’!
=>
8+‘

H
. 3




.-. —~-»
-




‘I

-

i
1



1
F7‘ Tg = lr\‘L-rhjc
I
A =_=7 >'"‘»(H+l§ =-|r\7‘.+ Inc,
IQQ1. ='lr'1 Qi‘
Q




=> lng = => |rW('d+l} '

'i
=v '5 = C1 =7 8+1 = ci‘
=v H—=¢X=0' x(5+1\,—-c=o
=7

~//e"‘¢e the 9e.nero»I 501- is (9-c;>Q(xg +x—c;) =0 ‘


I !
Exa 1
>LP-(x+X+&1)P+(x+x¢y_»g5){>_~;.3 ’
_..-.-.0

» ' ;S¢Dl:~ ’ 3‘

v




fince. the _qLvenle.q- £5 5at£sf(eci_ by P=1
1 ' I - '
‘ v

, J
~
.
,.
.1
1
/' ' B9 In

4'
= O X —X?-1*, -1I:‘
I
:O
Vv




X
:7 v(P"-Q (‘XP_73-X1?-3'P +1131‘) ‘ A l
X X El 13 .5
I

=> (P—1)[ XP (P~X)--9(P_1)] = O * +1?-a xg Q
I
I


~ 1=»(P-O ('P—5O(XP—g;) = O

' ='> P-I =9 50,,
' P-1 = o ‘or xP_9 Q: O. _ k



I ~




-/. 7H ' !'P‘_-.—‘|- (.3. u U P-—'>¢ = 0 ~ >'_F’—';J»= o ' >




otx — .= vp 1¢.i‘»‘_
A




OUL . » dlx ‘j
1; f+v_|o(y-dx{
- .| =
vde1=
_XdX Y_7
.-__.=%__
OUL
dg :
I



1
| |

'
2!
:7 Jdfj =
1 .




J0‘-X :7 I018 '=I'1dv7L' I

GU‘

=v g=>¢+‘¢ =7_ El7=X/2+c
2 J H “ST
:7
4




.
I ' '
|I’1\_-j '='|r1X lm '


\;;~7L—_c_ =0 :7 51-1/2A-c==o
=>
C I -‘F C
‘


' " ’ ' . =7 E:l~cx =o
J/erwcefh \ ‘ .
6'" 9e"<”-"°’ SOUS (‘J"X"C)(9-'1;2—C)(Ei-C1) =0
j % @’ Em‘ Y %




TRQ diff. eq_
=0 [5 £5O£Ol id be jg,‘/Obie
or y '



' ' car-7 be ‘Pm: i ~the ' form l

: " IQ V H=F(x)p) . '




Exm 53

_y0h-
%9*PX =P1x“
H .P1X‘l_-PX
' 5




.. Examle
% %




5 =-P211» P
V




—%l é)
’
@. SO|:-’ '
.




@ w,r.{_. 7L. we QQL QQ. @ w.7-.{;_ x_ we.

(ii; 3 2- ~ ci:T) S2E;i :2 T)l1_ :z:x:F) s2£I2_
.02
_
¥
P=F-\- (21P+1ci1'i 7_ ' \

__ J . ' #1»
|
-7 P = /4xPz+’2xl'P %~l;_7>__x Q_L_P -
7 ‘om ‘


on
:
V




' .




:V (‘ZIP-r + p_p Z
O
;J‘:> QB
Om I
2'" ’P<'*1>5P>—><0_1>2P\,;-9.” _ T’ %§ = P“?
*
L




f ! l otx O -_ 211%; A




I ' *

Document information

School year
4
Uploaded on
August 7, 2023
Number of pages
24
Written in
2023/2024
Type
Interview
Company
Unknown
Person
Unknown
$8.49

Wrong document? Swap it for free Within 14 days of purchase and before downloading, you can choose a different document. You can simply spend the amount again.
Written by students who passed
Immediately available after payment
Read online or as PDF

Sold
0
Followers
0
Items
2
Last sold
-




Why students choose Stuvia

Created by fellow students, verified by reviews

Quality you can trust: written by students who passed their tests and reviewed by others who've used these notes.

Didn't get what you expected? Choose another document

No worries! You can instantly pick a different document that better fits what you're looking for.

Pay as you like, start learning right away

No subscription, no commitments. Pay the way you're used to via credit card and download your PDF document instantly.

Student with book image

“Bought, downloaded, and aced it. It really can be that simple.”

Alisha Student

Working on your references?

Create accurate citations in APA, MLA and Harvard with our free citation generator.

Working on your references?

Frequently asked questions