Equações diferenciais ordinárias

Equações diferenciais ordinárias

-/~'\u-t<;Áo l,·,_,ecAf!:.: ·t.Ac €1""'é-t-o Oc°FG"flE.,,c.CAl tJ(2.0G/IA. .· popc <Ç'tX._ iÇÇtf2'fTrt-~.""--\. Co,..<-A..= ::

"-rvrz f (X) f: 0 l (;_ ,,v '( Âo A érV~ r ó r º /ê'.A/\ r1-

1 ~(:<) ~ i J L-==-"' .._._,

t ;V-(,;( 0 0 (-A To (2. TN-f ç & f2A NT C: É:;, l IJ ec 1'1 q (X) J i: J.~l '.l >kJC' .'.X~ ~ ""-e. -= e -::: r:_ )

,,,.- SolUÇ;-o Ge(2.4l StÇ/2A

----=-----\ 3 -3 -) Y::: ~-\-ex _J

/' (l)í flA-0 €: »e (2 A ~ J qcx)ti~ S 2 J rx._ 2x <! )A_~ e _ e -=

/l fQl u ç;;;; Gl!: P f L 1\ G ofl.-;4-fri R-4 v ~é:~"' r-:; l\r ~ + ( J )CJ'. )LA (-;e) d_~ -t e-) :: ?• ( J2zt/"édx *e)

_k~ )e,.,'90 . V~ y L ~ .--) \" = f\í "-~ -IV !}--1 f.JJl;; o ";;

E_j~~{ X'L-1-ci]

V::: _L --7 '< :::: ~J _ Vv ~ r , º • )é j?A-/2/.--~ Cx-xY) rJY + (y+ zv)d-x oca

'.X ( ' -Y) Jx-+ Y e i.., J( )d t -º

(\+1)Ji + (_L-*Vl Jv ~o .T / y j(Jd d:L ~j~)dy ~ e 'JL '{ J~ Ci }+ X -+ jf'A_ V~ \"' -e_

,/ (; [/fVLÁ f(Uf/f;; 0.t:A-:rA S-oM6!1J<\& ÇE)

~ ~ IB qY ax

[ f"!ZTANTo 1 E-Ki c;1,;;; u~ fJA>'f il"' <f{ 'X 1') 1 f AL que: :

µ li,\') cl :i -t )J e 7-,1() eh ""' J_ f lrv t <;. G (2 /\Ól 4 .f 6 0 U l, rJ '( 6 (:; r CJA-Ç e;_ 0 (31-1V -t ~) d X + ( x5+)""-Ci>) Jv ::: o r~tvDO :

M-= M. € 'IJ"~ ~ a~ iy ~J)A.~h-t tCV) ~ fN1Y+JC"<)

~::: jMJ:u icvJ =-' j(J~t) dt .tfCr)

viv j""-c)(\ -1: te'<' l =-Y x 3-t r.9-~C x J "' ~ex_ J

JCuA-L&-;v t>o ( J ) E (_ 2) ~ \U) .,,_ ~ u) -::: e t/l1Af/'ÍO J { 3 ,_lr-+ x_J.d:x: + ( y3--t !)""--t_\dr :o ci e Ir+ vfl,..,,_'t -tC( \ -= o 'f--

!),,.~" U"'-"-t'{ UA' O o ,,;cci<u"c; AL o ~J>ÍN,; (li" '>€ S €GorJ '><'-<>~"D ‹A'\ ".: lti(':l1Y1 Y1 ) •

Vlt (Z.; A/\/fs X 1 r J y l í r Çé { ;(. l'• 1 \"J) fo!Z <JfA f°Á o be fl. I €.,-J'Í (IÜ

Sr f 1 f')i 1 fr çio coN-t-c'f\Juf+S /\)V""'!+ 1>A':l\, (L<eG{r:, (l \)rt<;

{ fV\ 4L G U/Vl V r..L o ) (ro -A 1 qº .t-A_) e (o_, ft-)

~[-;t) -~ '\J(X)

\'' 1+ C1 J.A, U) -+ ,el'(,C x) 1 frz-c 1/ A--Y AC?'.) <: v-c ó('.) ~ ) /[ o µ_ -+ _,/?)A. -t /( ')).. -::

1\)\-f qf\J ~ o

Y::: C1 L + (g_ u

~ çJ1JSír:..r0\f.Juo (VP<; [))O~ ) ;/-::: (e, 1A .J.. C ,,_v-f+ _,fi [ C 1 )Jc -+ C 2 'if) + 'f ( C 1 ;.q C1 l\J-)

<('. -::-C'1 ( M li+ .fl»t 1 + tJM) + (' l-e 1.r' '.t f; ?P') .+ 1 V-) -:::: 0

VP>o~~ ; A ~ D1 . (f) ~ µ / I C1 { J) -1-µ 1-l+) e 1-r i d ) liY ç Li!-::µl1Ct)C,{;1-)tli,,(.1.(l:)

.As ,--- 5 ol u ç ori. 5"

[õo

:( f 1_ p"' f ~ J'i j ~ , J ~

";(""--t) ,JM(M-•)

J 1 J'1 ./ r ( ({ fi )A r-t () o w R oN_ $ Kr A fJ o !:> é\-s -

1':o,N IA?--1>v"s :> Pl-v ç';;to 5 _!A-,-v pi;: UMA-~ ·l ]) O L; µeff{l (t,v. º ~;; ;\J(A-I> E ;2 ~ (l/'{X.M. g,f 0 L <Àlt'.Afú/< e-/V °T iE i JV ~é f'Ft--Jffa -fié> <; [ 1 C 5~;,ic ){ :

fóL v ç-;; r:: s ..,<.A-( >e ') .ç:: 'lr ex ) !>e-u ('-"-A :()fl_j)t:/Vl t lf-ç ~ (<-.NÉJ'r-f()//€AfTC' P~te.1VD ‹/l.f/ ‹<;

(} )r;, ú Wf4J/f/5K/llfi/o fo!Z. tu;JTtCftMEAJ\C JJULo .

k-ftç 'f'u1V4~5 ~X _:,)Jr)('fENOC1i,1Téc; Ofi tD C? : y'~ r :;::-º

l Do DE"" ,,2_-G

'>e; t <;;'oM[N rc SE) for'> f W [ ~(K) 1 0?C><)) ~ ~~0Jx}-{~ X ){0,1<) -J -1 o

-;f µ~A tZMé.J-' 7 E t ;v \)€ f tZ-/0 ~ <E" rU t-e-S fu/JÇ;;€S ~ ~ K-:X. sr-o l" f {).; (1 1 (i' « ) :::: 7 ( K '.Z:) ~ (X) flée "' zJ--1:-:x._ == O lf x o .M t_r -r o O o ( lJ~ ÇoL-v ~A-0 'VA

,..-

fi Ç 'Í ?< ( vl J <( ~~ ·' N {+ E 1ú lt-Ç t't. D

------~ i;i-/~ ~'l-z-c-0 ]

{o/V'" 1/~-/ O 1 1f >< i loG o :

a 1\ tz--f l-~ -f e ::: O e 1/i</VVlD A-r; ru11 Ç'4;;, (,4&ACÍCt21 ~ t<'c A • [,_, 1 Ao: ";:-Jr!~ 2 q_

Pol?. -r11-,vf 0

J f o PC 1f!i!Jf 'Í€ fl T et_':; e:M o S D ( 5T:N-f 0 Ç :

Jf{4-(--zc; S (/{_fA ·ç f>(S71')0-t-AÇ ~
1 [(l.l MiiJ <; w t\ ') f' A f z_6 /ü ic; _t_D_is_1_1 N_"T_""_ç _:

li ~-Jlf~\JR__ \ l J>v!+S

' ,,- ) l!r ((P .,º

,.--._ A )c&urfJ"tc [ru~1 ° :

yt(_, 3 t)-f-~V -:: D l ~r n.z 1'K X e ---3 "'!tf + 2 e <;;= o

}_"--3 }. '* 2_ -==-o

~ = 3± ) :::[ X.t-:: 2. )_ -:2-:=. \

,.._ l ( U/1-Ç t'J-o '°

\! t _ r 3 \f )-f 2 {,.---=-D

J 'y 1 (p) _::::--~

Â'.l . 2-n ~ hz. Y-= e':/ 1\ e -5 7'e -t 2 e == o

t -3}. + 2 :: o ~) l , ~ 2 :::-!

..-9 =-2 l-t + C;i;

5:::: e,~ e')_ '---------

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