02a_Clairaut_Homogen_ExactDiff_ode

02a_Clairaut_Homogen_ExactDiff_ode - i I Feb 4, 2008...

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Unformatted text preview: i I Feb 4, 2008 CIoLtrau‘t *3??— (S‘PEdoQ Case 3% D‘Membflr’f— Lagrange.) , Us 7:. (iii. efj. 'flz'xfiJr . 4 h . 'D\’&men\iajcmj w-w-‘r- an. 1- 0‘11 (3%.: ug§L+ 121% + 443] ,. 0 ____,______. (k) Then an ’rwo No.6», 0% gahdfi‘mj fig W 7 Case 4: Reflulq.‘ we a" = .. _ 17%;: CI —’) 3%: CDHQrM- 6 ii Thug , is a sduhon '20? am. 6. i! 5 These. ewe sfialxjhk line; NM) 3-in’m-uzP’r 3(a). 0ch 'Xrinfixupf ~3£c)/c. a i l , Ear 9-3. if Gav 3CP)=[D9; ‘5: CDC 1121' is o, 0”"- Pmame‘h-Y' 41171155 0‘?— Soluh'cms- Tynes: 0m Q‘s-0.30% lint; MW» y-inferuph o3 & C. 6) Sign!“ Solu’ficm 0-13 = - 3? 3 4 ' ;; Then is one so\u\fioy\ +hmuag 95:0. 3:0, NNchh sxmyfi 37:0 (in shqifihh line. WM) 8W bu’ril- is m? We 0mg somhcm. gauge 2! 3injuloor 5&va Pino‘tMeT N03 cam be. Sohdaed {s b, \EMYB :——j'(ji)’ mm j‘"$ flTfihflfi) m This is a Faramdfric dPSCfiYHUnc‘} GCuWE 03M!) Fa'rqmej'rr LEHflj 3.3.=F, 'filfl Sde‘n HS 9‘- 7— :31;»), 3: ~Pj'qah 30?). in our emmple, fins Curve. 3;: war-2?, 37-131 _ 7. i-e; 3- ‘2— 4 * ® i Thus, 'fine sinjflqv Seminar) emreLeFes “WW. NJulom Solufiw. i t \ 4 1 f 1 VET'A‘S, jg =, 9L Cons'vadfl ODEs 0? M {-0er ’1 215 aura" = ,_ , Homogeneogé 03.63 .(qu‘re: d\fimen+ from “near homagenemg) I + (5/901 ' 7-8/3 5(1) = 7551400 d z: “I: '3‘ ' 0‘ = 3?; {i} 3 5—} VTTQhS’FOTm , u =1¥¢2 =7 ac. 3M5 d 56% doc ’x aka - 401% u, day which 1‘s Sepmabh. d? ’rcu)~u = |~u°' omd EEC — \Ymhjvodinj and é Q-u’jx. =1-c = Cone‘rwu’r f Thus The. Solufiom is “(11%; :. u and 3 =xflt£ = q/x‘ta' ~\n\\'u°‘ = \n\d-\ +3 '2. 1L 1 2203 a O: on + u, and “Wm ODE beam“ '1- Q'JL +C‘>o 2x+ C 29C 4 11-kDa 07 x°+ (x. Exad' difie‘fenhols amcl inkej-rufimfl , T? unAers‘mnd ‘Hne. conceP¥ 6% exctd' Aflhwrm, We wi“ («5% meat tsum. backgrounck "Rom muvfxsmnlafiie. New. CongiAu a Rancher) Z=F0cixj§ a? we gamm- Mav'salkes, x 3, L5. A ToLFMuQ @mm‘mbm a? such abruch ,ccm be ¢mao\~e. in ’hNo Wpu ,l} , A fifl‘gwdimensimafl PM A Wdimmsianafl Mum Pic? 1; _ ' Le} us 503 our 50mm 3(1), flies exndflfl on I“? Cam‘vmr. S‘wnr’rinj ak 0mg Pain? (1,3) an flue Con’rou‘r, Mm HM gum-hon VaLLe is C4) if we. move sighle b3 amounf “03.09) fhfi 3&4an Valwe will ChQYEj-fl b3 Qmmn‘} “H: 3 6117+ 2E)dj (Hub is an cued (Akfimnhafl) H Hus new Palm Is on W Conbwr, firm) GIFT-,0, sfnaL Prong. «m 7‘5»!— mnbur. Thus Hue Lonhur is described b3 i wwa-W MW e I l i 1 i: m l l @ ‘nVeanj HIE \Dj'lc, if We have an ODE 0*? ‘i‘ne “Form ML, NWMDI _ =3 = 9(3)? 38:13-0 such WatMggchng +0? Some hr)ch Haj) fixer) Jrha ODE has sulufim’l Hag—y) =C a Conshml’. gimme a Clutsfim’) is: whim NM such :1 F093) fixish Theorem: Tes¥ {tar exad-nesg (F3 63). Use * m cwoss-der'lvOiiws a?- F'. 7211 = BEE = 21! 33 3293 37c. Thus, ‘Hve \No'rk'nzj Pr’Inc'xPUL is, if‘ M -,.-_ ZN , ’Her 03 92:. 1 such a 1?de ) £13535, 33' (grim?!) 0‘3 “Sing dx = 0 3(35‘) MF's‘fia? N‘ %-sta(=%) QM = «053 , afl ,_ «053 =7 F ends. 35 61 9F” -' z =- * :5 5.;__ 3mg 7 F ISI'mj-r {(3) QE 2 «1.033 1-{3’t ) = —'xcos +2 a> at} )=2 3% 3 5 3 H 5 :1 4! flak 31+ 3 F=32+e‘%5iflfl = Consi is We eomfimn. C5D The Mask ques’fion is wha’r if,” 351.3}. Egg? has H +ha\- \s +he case, “Hum '11) cer’rain s'I’rvoiions, we‘ch 5H“ makl progress b3 mulfiylfl'mj flue equadfidh b3 an “in‘ffivofim‘ Eda”, O‘Cx,xj) . 0191.3) Magg) d1 1‘ 61393) N093) A3 = O r . The“ , ‘gor Hw's apress’lon in be am emd‘ ol'rHawmhofl, we Teflulve, E! a z 9 '. . - 93(6‘1‘4) BEEN) 1e 2?an 1. 595%] .. gg‘Nr age-l. I i i s I E €“+J£T 012:) 01' 0‘9) 07‘ 0‘21.qu IQDT SuhLabLe anJ b_ Mat“, N: (bx—8.23 I ! 3.11:0, QN=3 =7 100+ exact. ' 33 3x d (8-‘9 = I'--ol__—l ! I K Ler hj om inireijroflrlj R—adw 7(1) “‘3. o-to) = 2%,: .(31-525) J, «(3) 5) (31-9313) 39; 6-: O I. Bacardan ‘51:: Jr‘nis «Nahum, O“ olerds cm 3) hence. we have, Hatched Ox conkqd'wfim +0 om: .a$$umPHm 6% 61x) J TVS 013) Mb!) - , | 5%) + o~(ou= 0-9) => 519: = 35 => $14335 I 3 . 3 i @ ...
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02a_Clairaut_Homogen_ExactDiff_ode - i I Feb 4, 2008...

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