82A Engineering Mathematics
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1 Class Nos 5: Sod Ordr Diffrial Eqaio No Homoos 8A Eiri Mahmais
2 Sod Ordr Liar Diffrial Eqaios Homoos & No Homoos v q Homoos No-homoos q ar iv oios fios o h o irval I
3 Sod Ordr Liar Diffrial Eqaios Homoos & No Homoos Srr of h Gral Solio Solio: q No - homoos Homoos I.C. whr : solio of h homoos qaio omlmar solio : a solio of h o-homoos qaio arilar solio
4 Sod Ordr Liar Diffrial Eqaios No Homoos I.C. q f
5 Thorm 3.5. If Y ad Y ar solios of h ohomoos qaio Th Y - Y is a solio of h homoos qaio If i addiio { } forms a fdamal solio s of h homoos qaio h hr is osas ad sh ha Y Y q q
6 Thorm 3.5. Gral Solio Th ral solio of h ohomoos qaio a b wri i h form q Y whr ad form a fdamal solio s for h homoos qaio ad ar arbirar osas ad Y is a sifi solio o h ohomoos qaio.
7 Sod Ordr Liar No Homoos Diffrial Eqaios Mhods for Fidi h Parilar Solio Th mhods of drmid offiis Th mhods of variaio of aramrs
8 Sod Ordr Liar No Homoos Diffrial Eqaios Mhod of Udrmid Coffiis Blok Diaram Mak a iiial assmio abo h forma of h arilar solio Y b wih offiis lf sifid Sbsi Y io + + q = ad drmi h offiis o saisf h qaio Thr is o solio of h form ha w assmd N Drmi h offiis Y Fid a solio of Y Ed
9 Sod Ordr Liar No Homoos Diffrial Eqaios Mhod of Udrmid Coffiis Blok Diaram Advaas Sraih Forward Aroah - I is a sraih forward o o h assmio is mad rardi h form of h arilar solio Y Disadvaas Cosa Coffiis - Homoos qaios wih osa offiis Sifi Nohomoos Trms - Usfl rimaril for qaios for whih w a asil wri dow h orr form of h arilar solio Y i advad for whih h Nohomoos rm is rsrid o Polomi Eoial Triomair si / os
10 Th arilar solio for h ohomoos qaio Class A b a a a a P... i Polomial b A A A b A A A A A A Sod Ordr Liar No Homoos Diffrial Eqaios Parilar Solio For No Homoos Eqaio Class A
11 Sod Ordr Liar No Homoos Diffrial Eqaios Parilar Solio For No Homoos Eqaio Class B Th arilar solio for h ohomoos qaio a b Class B P a a... a A A... A is o a roo of h hararisi qaio h is a siml A A... A roo of h hararisi qaio h A A... A is a dobl roo of h hararisi qaio h
12 Th arilar solio for h ohomoos qaio Class C... os si i a a a P or ;... os... si ;... os... si i h B B B A A A i h B B B A A A b a Sod Ordr Liar No Homoos Diffrial Eqaios Parilar Solio For No Homoos Eqaio Class C
13 Sod Ordr Liar No Homoos Diffrial Eqaios Parilar Solio For No Homoos Eqaio Smmar Th arilar solio of P a s is h smalls o-aiv ir s= or ha will sr ha o rm i Yi is a solio of h orrsodi homoos qaio s is h mbr of im a is h roo of h hararisi qaio α is h roo of h hararisi qaio α+iβ is h roo of h hararisi qaio b i Y i i s a... a A A... A P P s A A... A si os s A A A... os B B B... si
14 Sod Ordr Liar No Homoos Diffrial Eqaios Parilar Solio For No Homoos Eqaio Eamls
15 Sod Ordr Liar No Homoos Diffrial Eqaios Mhod of Udrmid Coffiis Eaml
16 3 4 3 A Y A Y A Y 4 A A A A A Y Sod Ordr Liar No Homoos Diffrial Eqaios Mhod of Udrmid Coffiis Eaml
17 Sod Ordr Liar No Homoos Diffrial Eqaios Mhod of Udrmid Coffiis Eaml 3 4 si Assm Y Asi Y Aos Y Asi Asi 3Aos 4Asi si 5Asi 3Aos Thr is o hoi for osa A ha maks h qaio r for all
18 Sod Ordr Liar No Homoos Diffrial Eqaios Mhod of Udrmid Coffiis Eaml 3 4 si Assm Y Asi B os Y Aos Bsi Y Asi B os A3B 4Asi B 3A 4Bos si 5A 3B 3A 5B A 5 B Y 5 si 7 3 os 7
19 Sod Ordr Liar No Homoos Diffrial Eqaios Mhod of Udrmid Coffiis Eaml os Y A os B si Y A B os A B si Y 3A 4B os 4A 3B si A B 8 A B A 3; B Y os si 3 3 3
20 Sod Ordr Liar No Homoos Diffrial Eqaios Mhod of Variaio of Paramrs Advaa Gral mhod Diff. q. q For h Homoos diff. q. q h ral solio is so far w solvd i for homoos diff q. wih osa offiis. Char 5 o osa sris solio
21 Rla h osa b fio & * - Fid sh ha is h solio o h ohomoos diff. q. rahr ha h homoos q. Sod Ordr Liar No Homoos Diffrial Eqaios Mhod of Variaio of Paramrs
22 ] [ q q q q - Sk o drmi kow fio - Imos a odiio - Th wo Eqs. d d d d = = kow kow Sod Ordr Liar No Homoos Diffrial Eqaios Mhod of Variaio of Paramrs
23 - Sk o drmi kow fio - Imos a odiio Rdi h diff. qaio o - Th wo Eqs. d d d d kow kow d d Sod Ordr Liar No Homoos Diffrial Eqaios Mhod of Variaio of Paramrs
24 ; ; W W ; d W d W o * Basd d W d W Y Sod Ordr Liar No Homoos Diffrial Eqaios Mhod of Variaio of Paramrs
25 Thorm 3.6. Cosidr h qaios If h fios q ad ar oios o a o irval I ad if ad ar fdamal solios o Eq. h a arilar solio of Eq. is ad h ral solio is d W d W Y Y q q
26 W Sod Ordr Liar No Homoos Diffrial Eqaios Mhod of Variaio of Paramrs Eaml C ; - Solio o h homoos diff Eq. - Solio o h ohomoos diff Eq.
27 d d d d Y Sod Ordr Liar No Homoos Diffrial Eqaios Mhod of Variaio of Paramrs Eaml d W d W Y Y
28 d d Sod Ordr Liar No Homoos Diffrial Eqaios Mhod of Variaio of Paramrs Eaml - Gral Solio o h ohomoos diff Eq.
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