26 Maggi• Suppiniaueo are gcx) -

Keh "

can kite IR3 X

ESEMPW

:y

"

tzy'

- 3g =2 e

62+26 - 3 = 0 eqcacoutecesarue associate a y' '

+241 . 34=0

Az = - LIFE = -1+-2 if£

=D yocx) = ge×+ge→×- 3

gG) = 2e3× K=2

,V=3 ( t - 3.1 )

Ricexchiamo yp Mellon segments foemen : yp G) =CETylp G) = 3Ce3×, ylf G) = 9Ce*

. Tmpomiawo che vimeo.ee leg

9ceYt6#3eeY=2eY ←→ 12e=2 ⇒ C =La

Concludeudoy G) = Gextczekt leek

ESEMPW :

y"

toy'

-3g =ex gas =e×

,k=I .FI

Ji2eauasduhomedellleg.aarattecesticaSuoprestocason.ceecbroaaoypCx-CxexiyjCxkeext@xex.y4pcxi-eexteextexex-2eextexeE2eextfxxt2eext2fxex-3fxex-EIecex-ex-sLec-1-sC.gt-sypCx.zeZNoTAiypcx-eex.y

fg=ee× ul '.

G) - Ce×

@e× + 2ee× - 3ee× = ex =) 0 = et non W resce or

determiner C

- x

ESEMPW : y"

+2g'

+ y = 4 e

y"

tzyltg =D =D d2t2d+ 1 =D ⇒ ( te , ) ?_ 0

A : - I soeuowne"

doppuoi'

yow = SE×tsxe× Csf ,ER

- x

ga = he k= 4,

X= - I ←

aoedoppheCecIwaueoypGDs@x2Eiylpcxs-2exeFCx2tEJ-2exEx.ex2E×

y "pQl=2eE× - 2exE× - 2exE→+e×2E×

=2ee*

-Leexetxtexae 't

2ee* - ¥×+ex2E×- ¥2 2ex2E×+ex2e*=4e→= = =

⇒ 2eE× - 4E× ⇒ C -2 ⇒ yp←)=sx2e*

⇒ yk ) = czE×tSxe×t 2×25×9 ,GeR

Rwassumeudo : gk ) = Kett

- ypcx ) =Eet 't

set non e'

solution dell'

eo, ,

coratterast.cd-ypGy-Cxe.seTeweaaouoeoueseuplivdellbg.carodt_gpQ.CxseKsetEalureonedoppredcll1.eg.cacalt.Geuerolioooeudy-cwwecedrekoebbkweoaupovwoueiowixoligcowhm.alpstodi@srsccweuugeuewcopoeumomwooligcoeohMagCx7-eo.C

Pmx ) cos Sx +QmQ ) sen ok )

D,

or E 112,

m,

MEN,

Pm e Qm poeenowidifaadomem-

se 5=2 e 5=p ( ease Sco ) allow

ypks =xE× ( RmG) eosorx tsncx ) said )

dove Rn,e Sn,

saw due poeruowi di gaado N= max { m,

m } .

- n tubs gli alti was

ypcxs = em ( Ra ,G) eosorx tsncx ) said )

Caso PARTI Cohtrl : peer : 0 =D g(x)= Pmcxlasfx tQmaseuJxSe per es Pm = 0 ⇐Dgcx ) = am K ) sends +0 . cos of

u

allow ypcx ) = Rmcx) cos Jxtsmcd sen Jx .

i

ESEMP 1 . @ yi +2y'

+ y = aenx, go ) = sear .

- o

XZZX +1 = 0 ⇒ D= - I ad . slope

ypk ) =A senx + B Coax

gp G).

- Acotx - Bronx, y "pCx) =

- Agent - Book

Is- Boost+2A cos *- ZB sendtabak= senx

⇒ If = O e - IB = I ⇒ A - 0,

B -- tz

=D gp G) = - I coax

�2� y"

+by 1 t y = x sen x -

Riceeclraueo he whereon

portiwlore We found segment :

ypcx ) = (A×tB ) eosx + ( Cxt D ) seux

Spokane chesioe solution dell ' egoessegmata :

jpcxz A cos * - ( Axt B) senxtesenx + Qx+D ) eosx

= ( Ate x+D ) cosx + ( C Ax - B) seek

y"p G) = @ eoox - ( A textbook - Aaenx + ( C- Ax - B) eosx

= ( one - Ax - B) coax . ( 2A tcxt D) senx

( 2.CA#tcoox.CzAt/xtTDsenx+2CAtCx+D)cosx *

-

2 ( C Ax - B) seek*

#x#)cosx

t.CC#D)senx=xsenxeosx(2ex+2e+2A+2D) + seax fsa

- de orb +2A . ) = xsenx

2C = 0 =D @ = 0

2 ex +2C +2A +2 D= O 2e that 213=0 D= - A= .In⇐{→*.rs#x=x §I÷±Ii÷¥*a¥=D YPGD = ( sex - ± ) aosx - z senx

.

�3� y"

ty'

+y = I±×sarz× .

5+6+1=0 ⇒ a,

= -1*6=-1 t.EE Its ,p=Bz

gks = E *sent x

,

X = - £ =L, 5=rz = p

per cui coecbwaiuo he sdeohoue pacbi adore melba found

ypk ) = Xie £× ( A sen Bzx + Busrzx )Ten tonvioruo che we solution dell 1

eopuaoeome atseg math :

y pen = E *- zxI±×] ( A sen rex + B cos rzx ) +

+×£±× ( Ba A cos Bzx - Fe B serifs x )

y "p E) = [ &E£× . zI±×+t,

xI±×] ( Asante x t B cos rzx ) +

+2 [ e- £×- sax I ±×] ( Be A orbs - Bs Iseurzx

,

) +

+ XI * ( - z,

A sen §x - 3g Beos Bs x )

seurzx

¥'(

#s#x- BB

+→¥x#Ax) + easrzx .

eT×.

fHi¥+ is a-rzn##B×) + xnrzx .###r±Bxj+ eosrzx .e#×(¥1#fax) +Afxseurex.E4# eosrzx¥5 =

=

e¥×seurzx

sentzx ( - Fs

B)+ cos ,o§× ( 83 A) = sen B€× ⇒ A =D

,B =

- BL

YPGA = - §xe¥×cosBzx

aaudonon si e- in and delle situation a eui sr puo

' appliance if

matodo oh.

sowiglraume so mud proceeded coat meted di vorueveowe

delle oostouti :

Sianoysey .

le due solukoui di y"

tay 't by = 0 lm.

independent .

e

eeeebiaeaoypQs-Exx7ysWtCaWy.cxjNnpmenoloCheypCASrashenouediJQ.7taykxstbylxkffDylpCx-5CxiynQ7tCsCxykMtCLGyydxicsWykx7.Oss.cheseleLueicouifossecodellecostontisuaocebbecheCbQysCxiCLG1ydxs-0@7poecuimepomeudochevalgdmouesIudiaueoilcasoolicostauti.DaCD-Dylpg-Cslxly1.GstCsk1ykxeoleciviouuoIteceoemeute.yYpCx7-CbWyiktC.Q

)y ,

"k ) . tekxykx ) tSQ)y"sk]

Soshtuendo will 'eg . diff a he :

es'

G) yj Wt C , Hgh K ) + Cos'

41 ykx ) + SH y 't G) ÷t on GQ ) yslk) +

task ) ys G) + best yscxl + by ydxs : gcx ).

escx ) [ ys"

Wto :#'

W + by ,kD+ ski [

ykxhaykxitbyscxs.= 0 = 0

pecchi yse ysaouo solution .

+ gllx)yjcx ) tdkxlysk ) = glx ) dell '

eg . oouegened

=D CLQ ) yicxltddxys 6) =gK ).

Abbraeuo cost ottenuto A srsteune di due eqeeveoui con uicogrute Sledz

Cisc ) ysk ) + C ! cx ) ydx ) = o

{ ask ) y ! K ) +4k] ydxtgk )

Ossowaudo che bewatucedei coefficient di tale srsteaud he come

determinate 'D wzouskiauo di yseys

WK ) =

Ys# Ydx )

/yicx , gig ,

/ * ° ( ersewdo Ysey.

ein. indip . )

il astewaoewiuete serene un' auiaa solenoid - Dtteuutelefnebeoui

CLG ) e CLCA, integrand srolteugouo G67eGk) .

Estteph : y"

ty'

= -1 ( xtkti,

KEK ).

aenx

y' 't y

'to ⇒d2t 1=0 ⇒ 2=0 e f= .

1

=D yocx) = Cs cont Csaenx esker

Cerchiaueo ypai.CH cosxtscxsenx - Cuoeguesalcerepowered

sister£Q) eosxtetscxlseux =O .

{- ekxisenxekxscoox ¥

Wb , =/•× &×

|= eosxtaeeix =L

- seux coax

ekx ' =/ £ I'x/= - s ⇒ get - x

else ) . /a. °

- seux 1- / = It ⇒ escxs - enlseuxl

seek

=D ypQ)= - xeoktlnlseux ) sent

⇒ gW= Czusxtsseux - xasxtlulsaexl . senx ,Gf< ER

Riuapio oh.

aooaeppsrkom

Se gal = SEX tgdnt ... tgscx )

allow ypcx ) = ypsktt ypdxlt . . . type ) dove

tti

its - .

,s

, yq.CN e- someone pertucolare do

y' '

toy 't by =L .

ESEMPW : y"

+ y'

- 2g = × text I

y"

+ y'

- by = 0 ⇒ t2td - 2=0

=Dsoeumoii 1

,-2

=D gocx) = Cse ?tgE* , Cs , EER.

go = x text 2 = Cxts)+E× =gsHt£G)

gslx) = XTL powwow di to gzado

ceeeliouuo ypsk) = Ax+B Conte B costoeitida determined :

ykK ) = ft , ylbdxs = 0 =D A - Ztx - 2B= xts ⇒

{ I?FsI±s⇒ FEIEZ,

⇒ Ykx' ' - £× '

E

g§)=E× espowurcole can F- . I eleven 5 sdumouedellleqcoralt.

⇒ ceeebiaueoypdx ) = @E× : ykki = - ee→, y "pyxi=CE×

⇒ eE× - eE×.

2eE×=E× ⇒ - 2e= 1 ⇒C=te⇒§W=§E×

⇒ y•C⇒= ypskstypd = - Ix - 3g - IE×

=D yk ) = Ge×+SE* - Ix - 3g - IE× ,