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rg /a f o+ {.s hlAsi+MA E?qPuot t,leuR I A rnqop\KEr E=r:g:Eg Ie FneMoV Xgr voMENgN MernSntrriN I UT'^ =b v dg- =x d> vdx q"{-# :* 3o=i.^l*c :o yt=*"+c{ , cr --2c:o y=o,l x"rcr KoTuAaF*"- 01^ E^,lc Sr*1og.cu Eara.{Yw vq, &PqV*, Y'^ l't. 0t 7Q,x)= ftilj^(u^) 0 (y,n) ={"(^) 3 ,61) _lL 1'=3n* * .1t*'{t = dx --' /-+ J) = f l^#> ar( r tz J!''J :=+> t: x*C *:l = r.+c ':D U =A -L 5 xf,c _nx -tfr-tlu'-(4-*)u =.a *"(v-tl* dr-iU * *(3- {)dJ =(4-^1yd^ *+dt = L" d^ -, [(t-i)t =fC"-*) A* +J -8'!l=-*-0nl^ o /*U=I * lrx-U '+ )=et/* xda Cn.nf,61*n t .p.f; rwr Y=gC)) 1 t J U dy -. xlx */, a3 =[ xd^ Ir"b=[t" (uut ,) A, ") N, -] A, tJia^,^t Kwgrclft-vvrr.r F f"Rnr^,i pTr; PQ,x)Jyr q (I,*)Jn= o ZrS E *Oop,cr, {rou tnrrPtn1;.I^ va [p\or<o rllora, tt&^,t Au&a- fysikoblog.blogspot.com

ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ (ΘΕΩΡΙΑ)

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ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ (ΘΕΩΡΙΑ)

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rg /a f o+ {.s hlAsi+MAE?qPuott,leuR IA rnqop\KEr E=r:g:Eg Ie FneMoVXgr voMENgN MernSntrriNIUT'^=b v dg- =x d>vdxq"{-#:* 3o=i.^l*c :o yt=*"+c{ , cr --2c:o y=o,l x"rcrKoTuAaF*"- 01^ E^,lc Sr*1og.cuEara.{Ywvq, &PqV*, Y'^ l't. 0t7Q,x)= ftilj^(u^)0 (y,n) ={"(^) 3 ,61)_lL1'=3n* * .1t*'{t = dx --' /-+ J) = f l^#>ar( r tz J!''J:=+> t: x*C *:l = r.+c ':D U =A-L 5 xf,c_nx-tfr-tlu'-(4-*)u =.a *"(v-tl* dr-iU **(3- {)dJ =(4-^1yd^*+dt = L" d^ -, [(t-i)t =fC"-*) A* +J -8'!l=-*-0nl^o /*U=I * lrx-U '+ )=et/* xda Cn.nf,61*n t .p.f; rwr Y=gC))1tJU dy -. xlx */, a3 =[ xd^Ir"b=[t"(uut,) A,") N,-]A,tJia^,^t Kwgrclft-vvrr.r F f"Rnr^,ipTr; PQ,x)Jyr q (I,*)Jn= oZrS E *Oop,cr, {rou tnrrPtn1;.I^ va [p\or)- &x*c-> eat(g"\= "^o. ."*g^z=f"'oCK.e 'x'e7=? sD X'n{= e-tda,n rofto*,cX.e41'- ?oxA*t,l; pogl,as V tf6t =3O0' f 0.) ' 360 A^ 8rvl*dao., y=g(n) ^r a^,1nra&^ {q,., 9d- ve fow| 6*ton = U oyo6tu;a n ) f1,*^*lr o "rf*'*'(T)[onuu\\\rz AtneoplKez E=treNE Lg Bnonro\/Ittett"f A.r.M tt,^ntl)dvrv gQ=o.Of'n- Altfysikoblog.blogspot.com4doAotialeh" 6ot- "Frf*'ir a]; n^,q qp (T) U'o f 00y =O .rore...*= -f6V.-*+dt,-fd,rx& n,no9;vu,?urff uoruw t r*, ^af4ndvw Jlt fFO**yud cG.).f,-U=4xe*fla^g,* Trr^, T"trd , i *r5 ro -6' 5' 'J ( -p. ftra pr"ni,^.l):>ft=l Fp= +.dx =+ I+ot =f d^+ Iny= x*cAwrro^0rrlh,xtc- 1=e a'tt '1"r * lr?x,J'-e iKI"n='xIr=ei cx).clz\tl. Clx) +- feP'Ptt Auaar-> 3'r =o.fcc$ + {= - If cJ,t"t opg,,taris = C'efysikoblog.blogspot.comA orrtoas t;t)'tr,({te"llr_oYIa,(o.Me^!etIU+t*'=JJdi),).r)'d)Q*. 4r P"s'C= 5t..a^x+ cosxv'+ty'1 , Y(r)=b,Y'+2y'3O r !(o);6, $),ot3T=.A=.\)orI*(y-r)d7 + y("-r)dx = oo *11-r)J, = -l&-l)Jx--i- $A dy = - Cx:I) at,q-T- I -7rr=r> t^@o\y =-f@a^J Y -r J;'-> f )rar- EJr =- [4dx + [!a^Jy-{ Jy I J x'Jx'=E+ Y- O'y=-Qnx- l tc hvoq turs J.e C oe ntr&dftvu loflYafysikoblog.blogspot.com@ Ert,u.r [te1ln-r^, tnA',, t'to.,, E $ai E.a. foft"r.tP(*,1)+0(*,y)y'=o (l)Kc,tr [.^l 0urs t*t\nl X.tl.9&1,. ivct luxoro teR KcuP(tx,ty)=t1 ' P6,y) 1CI (rxly)= t s. Q(*,y) l(ira el ar&Jw :ngocnoh; v. t. s :o,P NovrSTuxoi a..A" rdKV A^, o\ a(tjzts (ora Eerrr-rG)= K.26,.)Kct^ ou?r\ca$tq,orwv (I). 0o ngow:yu 6.* E.e,. x.Y(' ft d,Fr61i orvof,Md\4' twdn.x.*y'+ y0,* = y(*y +y (ro 1?- o'rq foe\; n^^ CD)-',(y{"^- l{*y-/) * Jr= oP&,y)QG,y)p ( tx,ty) = t10," ( tx) - ty l" (ty) - t11= t(y {r(t^)-y {*6y)- v )fo.uory s, ocoush?otrru en"(\/= x'zrf"( ryf= 2+ xz' 0/t., {y) = {^(xrr'.1e 0rax - xz,?n (*a) - xz + x (t'r xzr ) = o+ x??^" - xz(hx +/.^a) ) F + Ktzr = o+ rile^r#K-x2.L,,> +^Lzl= c)+ >{/=7QQn?-+Xer =z(uVfysikoblog.blogspot.com=> t* :z.laz ,,-o-^!-dz+ f@Jz = lux+cJ / Quz- J*"* -o !uz=*rt^-,,

f*(^,y)=3^ty+2'e^ (fr-oso f,"'P* p'"* - f srvr0) = ps,v,g. Fr:rvrro+flcor +pcosotp'.osO-psru ' I ' F.org_fF-ncDla^Aaathf,,^r f. (p'cos0 - pr,r0):pscosO ( p' r,^O-t pcos ulptr,r0(p'cos g-ps,*g)= f)\v10 (e't,*On f co5O)* pcosg (p'.or0-pr,.e)*fuco:20 M*pusr,re0== f f 'snn'o+JlMo*fp,a;'O:>+:+dr=de-T- ?*rbrs@ IAv.^to9kntpf f".ts6 - s,q\ o)= f f '(s,fu +co*e)?*=r P 'r'=Ft-d.( gt ng) {-.-de-E=doTD ItG) ix-p's,rng +pcosDp's,ra0+LcosOgtcose - pfysikoblog.blogspot.com@?| -3 a?=lsg+lr , ).-o ;l -3+r '*.,-)tl f =utcuL^^ O+ c,-La o"= -! (o*rnr- vo' PcrA*.eiJ" e*)t r'(o*J \ Exr'^r a1vurusotXouq oa ntrrfs6livu \^of\*.ttt,*S= cosS**tOt*- or&): co!5(*)fiq or\n,-T2-zX +Y2 Z(e"ct-"e) + cr )fysikoblog.blogspot.comB/s lor IS tnPMOtt,terrrn U I4g u'ss6${nAtKr\il{ 0.-xyt*y = y'Irn* (-B"*'^\t')L: P.^trq A,o,t, t^z Y tx y'y-t + y-l = f ',n* 6Gr*, [-il]O ( oi*,.T,1** tu\r ]a, ux, nod*[.)on6J ?=zQ) ? z' = -y-1 , ty=r1(x) J ' 'o,ffiO__l23 p,;r". Awrur$or..,, druv (r) ru 0?t)\x.Cz')4 g=l,rx-zl.x + z-- l**@Fto. bc{varpyc., }.1. cdpot^t^,"r)IF* fr-e*o^ ]i,,,.^r -x.Z'.t?=o + -xzr=-2 =q xdz =3dx:D lra?= lqz+C1:p, el*a="1".x+",,o, Z= l*^ ..f.- ^e''=/a..{OO."tgt f\^ t^1,r.*,f A.ron fu: x.ck) 1Z'f = c(t+ xc'6t) JEnuS" 76 l^ep,o" Avaa rws G) o^rrrpo,$\cr(wttrv ?t^ ? ,'n at*u G)fysikoblog.blogspot.com@ -x[ c(x) + *.c'(*)] + xcG)= lux=D ->k6r\- x'CG) + $=lwxlwxo\x =olt< =/Lra\w. + ! =cG)XXEnoy,lr,.-s * =?o+ 3pAuf ",[" ]: cx* I rax+lo*-. ?,,-r* itttxw lu_no.,?do,,,.^.\l:D CCx)=-$*t/t)'l^,od*| \ xlIJ-ri"t Cr) =cG)= f]llJ-*!l*x -( :r Jf.*) ld>. t +-,o\x= l*^r- \,^(x*r) +crJ1C**t)i=t, J[* t^ :I'*o\x = I *,rx- l'. (x+) +'B=-t I Jl a)hwq O-ra_uOen^, x=jinrr 6\tuu0rrlsZf = xe(x)at.=.'.f**y' =*,: x(x+i))' =y + x(xtt)$ =XOn*t ent^&,xyZfA = tuxt trb n.A :(.x{o , y(t'l:osI=K lOrP.YxttY,:x+t*)' -*+dY=**r*x =?' f +ar=f*)dy*0.o t5 J*nu" Grq^, L:o \b.^ws') (-gdxz f@,) x(xrr) J x9"fo.-y."'I +c$)l'lnJtloftorrono\w-Ivw oqnAvrrr vc! *?rs Y Ifysikoblog.blogspot.com@ ,{-4r-, = -%yyd*c,Cv)JT=oTG.1)= saz?< t'*7 * *3), - * I. =.+ ctcy) = -y TD,c(y)= -iyt{" 3*do* Eray =of*.(- | urws oJ,tca,6,opg'o*)};oa -(raS D.z. otrun\.pt"n \^"ft y .a:sk\rs ( 31cA11 l) - s1^" -y'-e*y'- 3) - 3d*= o (I)0 Nq fraba 1o J wora t\ Y, = d* ) v61 dr'o'r tr lucur) N" 1.,0t, q 0)1,w! (t)I) t[, = 2'^ , I'n = -Ad* FuJ"*, NcLrh,.]o\^ 'r^^s CD Ooru^rtno) * &rbtr. Antt.r0ro,^L:-1 e^*- e*(e*)f 4{.l.'^A) - 3e, i e'=> -Ad^ ^ z*-t".f -3e-*A - 3 E*= o+> -a -lt^3) ^3 =o :o, ]t-6\) t3=o+ A,,t -4--t,fysikoblog.blogspot.comEn?au*r r) y=-3".?i;) t=-{" J4 P\enortrycr\Tos 1wg RtO, ALot s lrascqtti :Y= Yt*_t_7(? flo'r&q)n a Vl tnrlaf^, htcru I- 0 I t^.?,* {uo.aYt = -d*(n,urrr^ t^q,).ve.)a,rr,lc(Ao* ou* ft)AP":F _\Z IL+ e"g-e*( i ,ri-dl i.>l ,t:o+ {_r_{*3 ./^ a zt +ex a ^J.,,-,. ,\, z- zr z ^ /^ = o + zr + e' ^?=o{notrb* r" *1z- r t+z'+e* 4z=o +> z'-22= -e* Qt.Fr*), (+- d1 -3d*=od* = 2l,xz)^72=o =' Zt=b* fr=e= -p(\ft-u L\r1t1,l^,1,,.2=2xtCl. :m-fysikoblog.blogspot.comZ(= t^ cG")z'Vr=k'..fcc*)+ fc\Cx)et^CCx)= e *4" ?'r=e"*e-^=g^ >0n ta7 =?., f?p=f c+e^\ aa.5.a yCd= -d*+ Al'"CJ-xr1(x)= -g+* **".c-?*_x= ^8:P*,fysikoblog.blogspot.com,r+[tlot ItqAPttou{eun{l5z MAsHfr.,{ AAl AqoPtKn E:tr:IEtr 7s BAorroYr@Ies*.*yn+py'*6y={{,)o r.rv or,P,b *R ? S*T*.t Clo.lrrt*,qrrq", tw".,o ,flPtntH: Qto[.r,rs kTtarv"a ! .a. r o7* n F d, * try = *,F O*t ql'+ p) +g- o , : = i1,*dt,,r htra?1,,r,,' .tr-h^n Nn* rh, ot'* f Aq=o (t\\n\Dl\no Ta. A n^, fgr Arw )rcrrgvw 5 nrp.r,fr"r6&t ,.)x,,1..g[Ru TNISC[,olota vt t .'tt {\r'r tr\cr.ry(*)= cr.ot* * (zeet*), --Xz oA);. e Rt if,a(rt= "o- G,. cos (e*)* cz t,^(9,.))")cr) el'* (c.*5y(-) =ni"s.**\11r,Xz- gC, (HG*ra'n $o t't'vcr^fysikoblog.blogspot.com@ AlrHrH _y'LE'+6y=o + A'- 5rt6=oA--ZS -4 .t . G =!..=2 A,,2-- +. lt' t3xy t l^= 2A, x cos3x =3A, rfs,-}x t2Ar,xs u3x +3Azx' "r,r3 Xy"f -- 2Arc.os3x-6At xsln3x -6A rxSrr,Sx-t A, *cos3x'+zAL: nn jx .r 6Arx cor3X *G AZr.c9r3x - QA z xls vrn3xA.u*Sot;'- 'fysikoblog.blogspot.com.\* ) noAuri,v r1,^. X ErELrrr-,.rfc')= P,a(x). .F^\Z^^---*+/v" ,^ poft,^: P,n(*)=qr Xq + . .. + 61,1 f o.oYn= (n,*t*A.-,x\^-'+ . -. + A, **Ao)eF*. xF?TL' "f,t*tJera"( Tb P rto x.p/e. *f /t^^ -. f -&.('J*i.-y"-2rt L7 = o 4 h'-2At[=o + A r,r s t (E,n1r ftr ){r*Yt^ =Yttn=pafio6?sIflxY "-2y'*Y=Yo = (c,* .r.*)e*CA-x'+ArxtA")i. ,lF= L e^o .T\^O\^roFTv\rFt , p=2" /lfysikoblog.blogspot.comrr/slo+ \ ^'u*sH*.^t\E?rPnro:-$ilEn lgjA)tts u&"it ftpretr..r,satsOXL seao{C*)= ""fl1"o x 196^" ttrfr"-tnxP*G) ( "rswrOx+ q.cosOx)\p= 1"*t t{Ttt -(o OL url pi!,.r -(a\, xT. no\.( p:-. yo\n/rot(E; Ft.t)v) {6 cz(x)= - f{J e*+lf - - 1,,, (+tr) = -1,. [e1r)=-(LJ t*rY=a (:..) = lrC.e*+t)-xcr(r) = - l"(e*+t)t"= [t"c""*n-{.*- t'n (e*+r)Jfysikoblog.blogspot.com.tle[ot6? ruAexA4n!frsfqn+ F)"y "+ A(orrp)y ,+ By = { r*)orvxr a,F, A, B, {(x) 8**t.^n,Hzvihnxqna'tr%,r,(Uu* t6b?tf rrr.l---a a??aJg.^z g, tlr V )i&sl (**z)?f " * 3 (x+z)/ 'o y= oX+2 = et@+ d^. e*d t -+-@olt = a-'dxCl K+ F:9tJ'(il=-Udx=##-9Y'et'Foo\xYG*U q,-r^{ v\ ^TA(*U.,, } t* uf\r,fg, tcwra.r o.AuSSo)5o($= g(dg afy'e.\= a(v,ddxdxotf= (Y"d't -Y'd.). o *g" =(y u- y') e ^t4Cx+2)"y "* 3(:.+z)J' *J=oE d* (y"{,). r.* j"a.-v," a ty = o':-> Y'- Y + 3y' *Y=.z- Y".f2y'+ y =o!= Ccr1..t) dtAor.r.ostaui',, UGt(cr+c^lu\C*+z)I+ &@tL\ x-\z= et*, l r(>+l)=t-'ta -- =L=A ^1,I "rYdc-3o\xfysikoblog.blogspot.com@ 4zKHzt\,t No. l,Du \^ )'t' (t-*l) y" * xy'=oLn. Tra tte\"^^ [x="^flg;1- cxbt -p *x= -swrt{t+dt :-L_otxs,t tbVL)-- y(c*,+\ = Y(I)*FVJ,9"6 =y'(')= !gg +Y-=dY oLb = Yd^ clx 01, totx-/\ /r\'L({) af-i)_ *ff/ -- -'\t I !, __Jx d^Cr)ks n'ttY "rrvut - Y'*,"tswr"t---s."ftAvUrlr$rcrwt0.- "9J u - *J'=o :*(r-..1+,) ffc_ _llt\_r_ _\ srnt Srott /:rn1H*ffi=oYf =cr- IY=; J*@'Sl)9ntarlnel(x) = - Jcl-v' srn t4r(..,rt) Y=b-S rnth"u>+- cot31 arcw=tfysikoblog.blogspot.com@)l4E0401 Ynog BAZf,toY TA:B:or(x) y" *a"('t)y'* as( x) y =oO". Eine.* f''o).t. ?j,qr p,e Ao'..'Tott '9t1^^,y = )r.z(),11 yc)=yr(x) a(A)f?.x.*'.y"- 4*yl*6y=ot{c,, Au9tr 1L t^ ' \, '-r ' .9i.,^, \Crd = yc(x). ZG)+ y(x)= )*.?CJyr(^)= 2nzG)+ xa'zr(J+ yrr(x)= 2zGJa2xt'(x)+2xzr(x)+ xh "(^)Y^ G)= +4xI(-*)+ rfzq &) .A,rtrtq$ou;xz(Zz+4 xzr+>)z') -A xC2 x?+ x!' ) + 6 xtz = oa 2.*'z t 4x?.t+ xvz'r-8*z- A*z'tGxt?=o+ L{ x?'t x'{zu-q f e'=orc xjz',+(q ^ q*)z'= olegrr-u A"o,r J$)"qr\o ?tr a nra g es Oa,Mro, ?.o*C A,t.p,o; ai6^ l4t*Dun,iqXarr).ttvurOew"qr=zr Yr->.t^t= ZttJfysikoblog.blogspot.com@x3rt' + Ct -H x')n t= o62 x'!5 *4(b x')* = oolxx3 &r : Q0l-r\^d.x&&= 4 (*'- D"1^.+> \rntra 4{.d( +=D tvru= \*xq t 3- + cLD\.+, q,tH= x\ ao/^' 'cl-> z|G)-- (^ ,.u e*/t' .J1-l- *l*.^=l| [:"ia.o-'+f54-J*1 Jx-l.t =416F -a ,it*.-LA q.c-xfysikoblog.blogspot.comTg MAslr$ftsto( orf_LA PLAC E,EgApfr4olr.l[f.]A I.NX=F(t)f '(o)+cqL I f(r) J = I "*-n-*t[crr atli"a !" , I o ,{+o-= t'e '- o+ I = LLzw pn s s-E(-?L \{(+) t- L-L', J SIst) LI,frr)J=cLIfttt I ^;) . i ,'.{,(t) * cz{.(*) l= crl If^(*] If (t)= t-ldtal- -{@l-t--5tl--l:? I =/)|r- Joftalar 0Trtl EZL t{. (t) li,i) L [{'(t)l= s FG)-f(o)-s{(o)-)" F(',,) 61= - F'(s)oo\{\, f l lt*)J=F[s)L I {"(tlJ = t" F(s)Llr-{rt)l ('\ =Frnx Llt F(t)Ju,uu),ctafPtfrrnl = I i"{(o*t =[**u,,,rL J Jo Jofysikoblog.blogspot.comrt , rb=J o f (r^)3( t-d.ttt *J" t k-r^) 3(r^)du@ui) &4{= o,y..poto rF(f ,rg) (t)F(s) .GG)=LI{tt)lL IJ (rlTOnor, (s)=6(sI, lr(t),ryt*)Jl\AAvtactc)l 'l*[trtrl=L-{ (t) = r'l p(')1AlrutHY "-Y'- ') =oI I ootl = | -'t-J s-ae eo*= L-'l*ly fo)=3 Ty'(o)sl J- tY(s)= ollv"-Y'rtyJ= rl'lt Ir"1- tl.r,J -tL[y1= oe2 Y G) -s 7 (o) -..yt(o) - s Y(sJ r(r-t +)\ (') -3' - I +3: oy (o)53sry2=(luA=q , B-_3o (r"-s -2)yfs) = 3s -2* ](s) =3s-2sL s-2G r^ Tr? st-s -2 ixw3s-2|6fff-il=*+a+fysikoblog.blogspot.com(Aqo Y(E) =4l".ntS -2 S+lAr^ r'lY(nlJ= gr'l*l *ir'l*ly(0 =Eu'** ?u'_KPOY'T tSS rvNAprHrFlS^[+)=[(t-o)= f * t'qL s+f ^t Irrtll= do''.L J1^4(t)=H(t-o) = | e tcoL d t>-9r fc^"G]I = fir-Af u-" ,)tL J J"rq, y'o= [^ ",5fr'ud.t + (***G)e"r.t)" ./ J^ 'Jo. 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