(z.c) ooF x Exo zt . Dai x (u,,unJ R= (t,,tr) Cfiz 4. Ve\\ - PDF document

( 235 L' r"th ODE Ercct f{cvr r e\-w,2les 1 fefcrrltal l A.i" Rer"/f. t j 6cie,-0. (, to- lioiJ l ?nctor *etloy'. rhf?trc6tl (z.c)

ooF x Exo zt . Dai x (u,,unJ R= (t,,tr) Cfiz 4. Ve\\ 'f I er e., iAr.,r- a',ol couh'wuo"!(y bZro 4t {uu c f,'ot 3 tRt /1, N : Q+ the ebE .'b tt e (t,, t.) + tR l: val (t, yrt)) 'o 14 l'ny luft, ,'lf exo-c 13 t h"hts \, N tt,u1 t, I LN )t /t )_/ ln tlr\ = ),r

\ 'I ot)E exort,l tLe Stio'r,, th{/ tr I 2t la> o) lh) + t l4(tt 2t 5o(. Lt +/r J LrryT I I' --" ,, N (t,l ) M(t,l) Jt (t,y 2ty 2l Nft,Y\ ) zY zt tlz t,yt \/vt(t,r) ^( o0E 7he o0E ?-rct h . 7he R .5 \. O!.- ldgPc- . ,5 r.of Sqaa'-*51..

Y 1 obE a Fxurr a{e . ?ro. / th.' t ,t "'.l v' - t' : 5in (t) - Y cctld -2t t'2 f+ . so( / . I Yc'lttt + tf etl =.: [s;,,(tltltaY-rl + t' eY Nh,yt . ft I -t S(v, (tt Y .dt ltl /4 tt,Yl = tel t2 aes !t) a 2t €Y )rA -- ooE at cxtcf, ,

,J { the obl Ep-, p lP ; bCL,. €xcc / fr, Y + bt . L l' . 'e[tl 5o(r - b/rJ] lttfo-a1Y --e t-{ ) . I Ntt'Y ,o ItN t^(t,Yl : o"(.lY rrA -bl?) = 4lt) '.lal I o r.lft t o. lhc oDf .'r u"t c f ex" l"r

.t r R c{r/ e r 3.9!!- €"9:. s Jt ((c r eq bte z'i ". The .olrt.rsouJa), tV:R-oP {.rv'cttorJ s.,t, r {), u) )t tV ft, )n M {t, tt 1 it( trare tvtc e ex,rtt \ rar olr't{ e t t* ble con i,.'wu ou t /y fuuc f, ou t; R -> [r 1a f,r f7r',1 ),. a rt,uy \ 7tr,'.t 1.. ' )r)u (€) s.'pzu.. A P-.f , \til lg t-' )")tt _- l )nM lo. (=5 ) o,'lfrc.lt ,' tl c' , Potv.crr

{ oDt 2xee f Reco"l/ fho. {S thr) t y' 2t/ =o Y2 I be ac-\r J e 2/1 2tY N' )tM l'>'tru=srvt 2/ J, . 2t +yz /r\ I 'y4 at\v) ,r v, .S" Tha fqv c f,, f,h,S zaJc .r, br.,r q ry /vl zt J e - t I 2t lr! ' o! Tte fc,rod.ru t to ce,tc;o.l k-o/ twpltctt E. t" DD J./trlrors t tr.

{ * tb!, rirq.lf Thrr'r I The /,(t,,r.)-+R te e6E the €xrct (t, Yct) =o A tt, f/rt) t Y'tt i\',ptft(try ry X tvP Yt be (t, ytrt ^t' ) t R {,.- < ti ov Whera -o [Q at s. t,.r 'r.l €y, l" a/t )r "f (t, al M /t, u1

.l l'+M P.oo{ =O .' a er,tt! . tyA thet ccch \N ))1= )t7 -- A f5g;4 fore r v' (trt) 6vr) 7 o a [ttt, yn1) ,tt t (t, l,'J) t

{ I r-!yrl? , f <) ttfs. I zt + y' -o 1 lt I l'+ Sl( t el. th . .,^,a fL- f Rp ts €t<qt f : => \r/ = tl Lty trA . zY rq: s> 2t t Yl fy*7 ef .'t s"-6.r f,\r.P 7 tt Ther , d) {,'. o/ (tl (t) )r? 2t f ') (tr"t\ "ty 2t Y 4f + Xl{J v t t x(( dy t-t = tft) 2t "fh,v) t {

.q = zn' l: I "^,' (r) >tt /f\ f^, 1r zt 1/L = X'rt) zt ltnt, tl ' tt" *t^ l ere f"te . l'tu,v) T'h o$ Thc ("1.. tt\ E s* a't f,|. E o" ! c Y fii It yY,, . t' = " I eclR ('n p erpfeSJ.'ov,. !;6;t ( ^f (t, Yftt) -- c

itx^-,,te. or. Ft",ol el/ : ?' Sol,r "f (s.- I I cts(t) u\ 1t2 eY -r) lt t P2t /=" t ("J. r. (a th. e?. It,.t c t Re t't CXa (rvr ft) + t'e l/ : -l - ."ttrl + ^t eY I >ru f | coslt\ +zt€Y A-- -) \rA 3 co!(tt +2t eY ? r/rr f,yt rr1 there erts f, s s TheFefoFe, u/ (tu4 t (2)

{ .tf >/ /t) =) siv /t) + t2 eY -l "| nltt,f\ ysrb/r\ rtze'-/ +1tt) - (e) => )ra =M +1'tt1 1et €l I co| +zteY /t\ | .os/ .ott ttl = o = c. \(t) nf (t, y\ = I f ) S.'t' The"of,..', the tolr s*tt €y . Ittt e, Pr A5t.cv1 . iv,plioit

'{ ('z + 4a v,a r,r lt weth,{, q J-rr flrrc-lr's er;rl Uo,.- Cxa. t lhera ODF tl"o.f a*r bg lu lo couves teJ ex'.et O,F b/ "." ttt plyt" 7 apuo. lte f..ov, ,rppropri. le f.r- e f,,'o 1 , l.cf ,'!'l for. f,"c ^rf,?

<5 obE r I I ttn I Thrwr l- tA l'rt\ , I N{t,Y) thY) L -" ] fhcf aS hof tJ ) I /v1 I I \/1/ *)y J fu"c f o,io( a' fhd I L )/,\ft,y) _ )tNtt,vt l avl o{oCl /eperol l/of luc- fsp", t\e € /ttt lvtt,vt Y' + ,t &) Attrl) = u ,'s ,5 Qx'tet , whdr, ,/4(t I . I sc/* fr'cu -)/""4j1' /'(.1 = h* L \Aft,Y1 /tt)

( i""' o'( ;:g:r3, l e?. 3.(t. I I r (t2 +tY) j l(+t*t^) /t--o So( ,' VerifY the el. rl ex,tc t at G", oy), t' t (sr)+ =O /') l---------------1 v zt tz t t I + !> )tft rlA z/ 3t lt /+Yz i l',.+ 'il 7Ae 61. . lVof ex +e t . rl

.{t N ( >rn- 4a1 l- (rt+ zt) - tzt +y) (t'+ tV) ( trY) (ta + t , (t+u1 t ( t+Y) :J- t (\yA -)t,V) - 1r'r.y'Pp.'bJd \f of ,) sc( ' eftr ls So, thart o* /(?) (+n- >r,,v) =.! l't*l EJ- t N l-;t------ t lJ- 1 -- t I ll -

.(| We ,'vr ./ fP?.a t/r1 7a.for Lat olv {' J? L,7tt1 l-(t) -- /.t , t f I by l"t f,h6 ertltv( /qul 7ly 4E y') + (rr'r + t (tt +t'v) lt FO ex*e ( t Veri f,7 tt^nt f,trr' vtew dE .5 I ztl f! tt'y lstV: 3t3 tt'y r t y" r ztl t.A -- 3 f ' >rfr = lrfr

<T (t,y) = o h1 ft 'Y\ Sdt ae c v./ e exe t , Solu al trow 4S q o-/ fhe ct 't so/. of, (t) (z) (0 =) fr rf: y )" nf= t^ Y" L (z) ': gltI+ x yl+frr*1 -- ]f,ty+ f y. 1'ftt * o --e ll',,