Series Solutions to ODE - 5m Sowsz db Wham-rm 5909mm m5...

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Unformatted text preview: 5m; Sowsz db Wham-rm. 5909mm; m5 mavensmm. seminaan we news; 50:. van so Fm: flu. Homeowne- _ Son ofi 31.658201: '. m.ch Iron REmewg ms Ewanom£q war we can JUST mitten»)! Rom 3:05: Ira Sow? 1.616., Foe Lmeae sensuous suou . 55 Y ' +37 9" 8"" . nvumvmc on? com ms; 8y 1m? macaw»: ' FfiCTDR- ftp-X) .-. 632‘ TURMS‘Ir aura gruff -: ex, .wmcu: «:5 can; ' :meGQATE 705mm! Svcn--mlc1£$«- Smny nan-1 5x157. ‘ W ‘ I LOOKFM :9 Sauna» y swam a: h Ruse-games ' - ' a . ' . «'6 a ' ' I“ Z ‘a‘ I 31 'JI'J‘ST- 50857179171“ ims now me EWHTIW nun mywcj'o ‘DEIEEDINE' me coemuewrs. aha, ,‘ c; J I - I we mm. mm up «am: a raw stoma amnpr m? we sue-aw Imm- _ how we saws am 1715a: m5 was flat «35' mo var sows may ovum-7 “RY . Exan'PLes _: L y, ' 7 "' a "35mm 171397.70» new HNM um ' ' To sows was. ) j” a ' . LET y -.-. 2: ca); . m5” 4': fl 7 a.‘ y' = 2 “C476 «flu ' "M 5"“‘WWE 3”” W 13555 9! AND W )' mare-me 599mm» ya, go mm In For m Mae 0F we summon masx no no“!!! 3 : ' ‘9 on . n a , x n- cn‘ 3 0 ' Mu “*0 -. : flfio a. ' _ x“ - a E mh’ctu ' en 3 Me ' :1» FOR au. n? o _ = _ I I m” ) can " C:fl a _ '7 " --’-- ' nxo" .Recannsuce EELHHDN : -c,,-,, = M, _ 6., F08 {LL ' ' «mm THESE our rm me any 11:5“: unmet; of. n.- I -' - 4.4.. "a, ' 'CI. = '5‘:- ' a l Ce L . LD'I‘LC a: .1 'cs : '3 ca ' .3 .1 J a . _ - - .J._LIJ_C "‘3 : cq "' “#63‘ w 3 a..'." _ .L. a 7 0 ca . Co I . I I a 7305' ' _ do _ a . ‘ I y 3- Z Cnxfl = _7 Z ' I I _' ‘ «to no a: '. J‘- 01 = co nfix .M“ 111525 J; mommc m Dem-2mm: a, sort :5 nmwnny, m any gnaw; ,pf a; ms :5 a. subway-Ia 111534097763 y"J/= 0.- . . I ‘ W a I a . x . . ‘ - I - NOTE : 5mg: :3 X = e “30 711E 3109:0512 1":3 Isms As :05 mm». ame- 69711!» serum: ' =:' '60 ex ' c ca: Mmmflywmm) c use? me renown ) Panz- RE-WOEX: n= 34-! (94:12” mm 45:: , I _ ‘ _' _ 1-: an“) I 51:1 :5 n: a _ , on n . _ 'f" z Lngaumncnnj ' nap - Nam SGBS-fiTDTE'BDfl! y mun y " Imm_ Inseam-17m y“*y- g a t imam a Fan we N905 or we mama,» Wm w 5073 ) . on "-7 «3' "d _ cnaazan'nJcnux _+ 22an = a ' Il=o . r - nu ‘ ‘” ‘ - ‘ ' . n Z: [tn§;)¢flfl)cfl*; * c." 3.): = a. “:0 . ' ' v 71? ' . cmucnu) Cm; & ch. -= 0 EM nu. 071-0 'REc‘DPRENcE' RELRWN '.- ' . ' l ..' =..-—"—" c -FoR&LL—n‘h'0 I . cM-l Janna“) " - , harm: Dress Our Fm mm Few umuss p: n : fl: _ _ __ O v a C. "3} C a --'—J" c I 3 3. I .L. - . r “E . q u - -—-— 1 I 40301:. CO I“): 3 = . —'-- c :. ._—-—.' 5' 5-"! 3. 5.11.3.2 CI 3 ‘1. s ' +qu'l-c x__ 4,... ._ _ 2. 7- Co +.c,x}czx;c5x 5 : Cb-fc‘X - Eco; —. 3’1“); 4- W cox 4.5”“): ...,___ it 3 J. 5.; _. = c,[ 1-31;“; :3: -..f.] 4., c; [x-;§x,.+5!x “.33. on a, ‘ a - ' 3% tn) 4 LI = C 2:. 5-2- x + c, ————-x ° 7 13,4)! :16“)! '&=0 7 *3. rum :5 mm»; 122, DETEane c, sm- a, so my 335.333,,7333), ._ F91? 8N? GIMME hr c, fin») ct m: :s' 3.34.51.91.25» yf‘gy = or ‘ AME:- smcs '2 -'-e-, X -= cos): amp 39 _ _ w m 16 _ r _ ' L“ x H a mm in THE 9A!st :5 we -A=° Lum‘ - . . I sang-.5 as :05 mm nape comp saw-:52 7: f '7 = a, cosx- +c.,smx- _c c, , c, amnesty ) _ 3. _ y " - xy' - 7 = or {No-NEED mpnsreno. m 0,...“ng ' Hon-:10 sows nus one, 3 - LET y: gen; ‘13:»! I. w “i ’ . a" y -.- Elm-4.x nun Ky = xZRcax is! =' ' v - a = 2.35%): El ‘49 . _ - -- a. at Y» Z .fitflqlac'fix J Imnuavrucnux an . w . mow sass-Mum Au. or 13556 we we Eauflflom _ 'c usma n’ns m 7 sums-mom woex w an or WED)... - n" .-'Y = Pf I ' ‘9' II _ - n- , ' - r . .n .. __ r ’ Z chi-aun“)¢fl.ax ,- ncn X. - E aux r... 0 (3:9 I ‘ ' . ' _ll=l- I ' «=5 . - do a D. V a tonne“): x’ .+ (trunniocnux 7- Zilch . . on, n“- . - J a“ r , r . .g. a ' w _ . h: I _ . . n (alga-mo) _ +32 [pm-aunfllcnu .. nan .. a“ 3:; .. a- ' "flu - . . I - . «I .. . I n . (5gp;- ¢,) + Z Lcnuuqn) can - m;.,cn ‘Jx _= a 33-! ' ' . '1'? . I.‘ «2C:- -.._cb ‘ =‘ _ regi11tfltl)lcn.1 -..- {Mach o_ to; an. a; O ..=> .- n . D .- ' 'L H 3 1- ’3: .‘hc x1+c x’+--- COJC,XfC_‘X +st); 4a.,x +953. ‘3: 1 . a I ‘ _ _‘ _ 5 .l . . 2 3 _l. 'I _L ___..... co " an” *co". " 3‘9." 1+3“! 9a." 14' 3-: c' x. HIM cox 4." —1-—¢-x7+_'__1_¢x ,. 363 ‘f'§d¢a° ’ ‘ ’ I DO. . . co [ I 4'5": +23%" ’43-: x ".4440? x " J _' - 3 _L"5 I" ‘7. ___ .‘I (“[1 4. é-x + 3.5:: J (‘5‘? X .1- ca. ‘Jco "a I . ‘3: 3L9 ., 7 _. J. ' . nr-"J. : CI, '1: c1 ‘ gap Co I n: 3 : c5: jcs‘ 3 3‘ at I . _1, _ __L-rc 11.2.. “I : = ' 01.4.6 1 ‘ ' I. ,4. ~ . ___.. 0': 5 I 3 7 3.5.7 I 9 __H_'A,.,7_.______._.‘_.._n__rA_. 4. A MAMA AI“, AAA“ngwfluflfiwn _ .— NOTE WT . c ' P — - an il- g,.q.a.g (2-3314-2 )(4-3 m-q) 2"“ *1! e _ 2-94 23.3! ;.3-5«'7 ' Iva-3"H-5-6-7 ' 7,! AND 50 ' 2'2 1 a a-o t 2-: x _._._. 4- —-- a 4- 3‘ 7" Ca[2°o:x .2'1.'x +2”?! 43’ I .2 ‘1' +...-- 4' .214: x 3 0.; . J,“ 3 ,4 .5 .2-3 _-.. I'- C ,2 Va, x J» ____x IL '1 Q x + ' X i- j l L} I '75 (D Go 1 all, Qfi'fln’ Q’E‘}. : Co ganja: X + C' {Rafi-H), ' 13:70 THERE as Nonmg Ta DETERnlNE to an») c' 30 THEY 13% fiFBtmfiPy. no i 2% Z a " ’ NOTE : T7115 TIDE 771E Fuwcnams 3 a: co 4,; A! Lg“ A‘v'o mu» _ I F159 _ £2“; . ugh)! x cnwwar 36 05mm wITfi Hwy Sin-PLE- conswrimu 0F ELJSHENmRy Fumcnoms) 1307‘ THE)! BEE) NEVERTHELESS J PEreFacny Ewe Sownoms To 7775 D’FFEPENTML munnom , Exsrmsss : " mm semzs sauna»; 19 sec» 0F ms "FOWNG amt-525mm. Ecuanéms, want me Amman: M: Z' - mammw. ‘ z , i, I, y +y - _o .2. y"- + 9,; = 0- '3. cx-uy’ + 2y = 0 n 'L y 442y"_+2y "0 Sowmms : Isa on I‘_fi_' W W} Eng“; -.-. _Zum)c”x g. nap Q ' a n c = 0 Zmrncm X 4- E :1." 0‘9 7 7990 g . _ n _ , E E tJuneau- " c" J x " a Q «to .- _Icnn)ch-H 4C" = 0 , 0 W9 - I can ‘ 3-3760 " “3’0 - J. 0 : c; = ' l (‘0' r .J— " 7C; =. " :11.- c'I = 1'1 c" . - .1.— 1 o. 3 " é. D I. ’-z.’ l I. - - - ‘——- c '3 ca 7 ‘ #‘c3 ' 1-2-3"! 9 ' ‘ 3 “ . c +c.x +c,x‘+c3x 1-qu *" : Co " 7‘0 x 4' 1712'.- cox " 1.1-! co l-l-fi‘lcb - ' ‘I ' ‘L l J.- 1 _L 3 .1- x ., .qo =Co[a’E'u’_‘+.z:"'3!x+-' ' .m- - h .- '7‘ {PU NoTE. THIS is C e 3 an 3- x' ' F“ a flip . yu' +1.1, = 01;_'- y 1' cfix fin) -_ .q‘ &" 'y'.: Zfid’ifl‘ - 4.21 ' a ' fi-z y" = a&3"’c&x ' =11 _ '. up . fl 3 2: wraJmfamnuxf “30 10. . '1’. an a - ' n Z tleJco&|)cnux + *1 a“: = o I'I‘O - ['39 a ' ' ‘ n Z: [muMa-ocnu + lien 31:: I = q =2, 01.9 _ _ - tnn)cn+t)cn,l'+ ‘Icfl :o A 107,, cm:- = -' 'mnunm “ a "’I O “9 ' - ‘4 ' 4-: “a _ n- I . c3 .. cl '- 7 q .- v" .. - - - -—- c 2 “'4'.” ‘cw’.- mscz' ‘ -g . , ' ___, -_ H" n..- 3 . c5 =' I” 5-, c3 ' “5.4.3.2, I E E . A z. 3 I: '5' - y -.- ce+ c,x_+ C‘x- I+ c1): +6416 4» csx 4... . ' 5' J ' :L- . z 4 3 'I‘ “. .15. - c. Wt - 4:9" - 3'51” -* 33"." *, .2 °»" " .‘L t .H" -t . . . _ L 5' - .1. 3 .1... _ + c. [x 3, x + J! x 3 . Q on ' IL &- c-llflqi £3“ at)" ‘1 4“ ,,, c ...--——-; X a C 2 ‘-u-—-—— x I ‘fl*"l " 1-23.)! 4,0 - _ a” I ' ' 3i ,9": -°° 13% 41‘; on c“) a -)A + ‘ i- c ' W c x W C X.) + Z I = Co E 11$)! a? . “I‘m-m ' fi=o' fi-O . _ m Nerfi : mu; m C 697.57 ems” ,2, I . I ' a r ‘ "‘-"”’ ‘7'" ’ ° .' r ‘3." a I y, a L._ac‘xfir 1;! , a L: Lx-IJy = tat-I). Z Rc‘x l=l II fl N i? :- ' _ ach- - 1 I s: “h 8. £3: ‘3 to ' a do = fic‘x - Z: a “if! _ . .31.: up ' . '0: = zzzlycnx” '_ 2E1Ln+n nag 020 Q Q 0%! '930 fig, q, to r» -&- n 9 ‘ a o . Z: nanx .. Lama .x - Zlmum + x +4031: “SI .fl'ul " n + 2w . nfil' 2 g- c,_+.tc°) + "ELM" - Lfl'l'13Cnh'l'1c-nj-x =- . 1’2! _ Lea. + act) 9|- Z: [_ mum" - cn+i)cn’_"] x = 0:. 13. 4c, 9 C .6 a: “1... 1. ) 4 a. It . .. 2 C C 3—,... l3 ._ a. a a c c. .. = n n cawcéuma was 5' .J .m. x ..r q K 5, + 3 ,K ..u. .... tx. an“ 3 .K ) .1 .I . I. x a a 15 H. .w. .... r... . _ o a C.. C = :2 VI q. :0, an “a” _- . y’: E 34:43! am: axy’z - n "=0 7 Q , i“ n . I n _ Z: ¢n+4)go+n).cm1x 4 Joan}: +- 7“? . .- 0:; as» - ' 0 . § ' + c x + _ mu. 2107+)73CNJ'I4‘.‘ J. , in. ‘ cau)mn)_con +¢tnnJ¢n :_ g Fara: - c“ n-Q-l £37 2 -- g- c. In: .' c,’ s "’ a; = n‘ 3' “5 = ’ é“: = x” ':. 075’ b °° r n a, Z; meta.)an CMLX L LfliJJtanJCn’lf Jan-+04“ J x“ : p .2 “=4 . : - 3’— c - -5. _.._..""1"’" .5 "3’ C‘- 6 ‘1' 6(1] co)” 7.6.c, z. 3' '- 5. _ -3; __...‘-“ . __—"" c "‘5 c7: " 7 c: “ '1 3-: c“) ' 3.5.7 ' A. .5c__ ‘2'. fig-C‘ e f' .9 w. 1’ E'xce't’f Pm me FA¢7¢173 a; .-.2 we PanERN HERE 1: exacnx m: 3905.951» Exams 3, m6: 3. _y-: C, [1+ $5??? 4* 3311+ £3.11. +7.72; i... 431-. I a'.33‘. J'yn . - ’ ' '3 (-23-.2'11.’ 5" + c' E a! x 3. 5!” (-21- --3.' 7 4' _—-‘%——'- x +“"" J . 7. __ z 2. - .3 3 _... 5' - (1),“; x; 4 (4).; x», -_z-_1)--2. 46 4 £_%_£Tx*m] ' co I” 41.13 4%.?! - 23:3 -1-"" ' I ‘ - ' 2'2 1k | ' I- A . . -.z..z. 4 ('l’olao I (W')'J'-J'm'3x3 4 '! 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