Mapa Conceptual Ecuaciones Diferenciales Unidad 2

 

 

9499  

NA^CAFKMNQ GFONYNMAFCENQ

3

 

 

9

 

TYNQNMWCAFÑM WNAMKEKJFAK MCAFKMCE GN @Æ\FAK AC@T^Q2 FMQWFW^WK WNAMKEKJFAK GN ANYYK CR^E. ACYYNYC2 FMJNMFNYÀC TNWYKENYC. CQFJMCW^YC2 NA^CAFKMNQ GFONYNMAFCENQ. AEC_N GN EC CQFJMCW^YC2 CAO-464>. 7tk QN@NQWYN MK@IYN

GN

EC

ACWNGYCWFAC2

ANY_CMWNQ

K ECRCYCGNE M CE^@MK2 @ÆMGNR MKY@C QCMWFCJK MFAKECQ. @CYFCMC. MK@IYN M^@ÆYK GN AKMWYKE2 94>4439?. MK@IYN GN EC ^MFGCG 92 NA^CAFKMNQ GFONYNMAFCENQ GFONYNMAFC ENQ EFMNCENQ GN KYGNM Q^TNYFKY. MK@IYN GNE WYCICBK2 @C @CTC TC AK AKMA MANT NTW^ W^CE CE GN GNE E Q^IWN@C 9.3. E^JCY2 WNAK@CWN, WNTNWRFMWEC, _NY. ONALC2 9> GN @CYRK GNE 9499.

1

 

NA^CAFKMNQ GFONYNMAFCENQ WN@C 92 NA^CAFKMNQ GFONYNMAFCENQ EFMNCENQ GN KYGNM Q^TNYFKY.

9.3 WNKYÀC TYNEF@FMCY

9.3.3 GNOFMFAFÑM GN NA^CAFKM

^mc naucafñm naucafñm gfonrnmafc gfonrnmafcee krgfmcrfc krgfmcrfc gn prf`nr prf`nr

Ec na nauc ucaf afñm ñm.. Nm ns nstn tn pu pumt mtk, k, eenj eenjun un`k `kss c umc umc

krgnm krg nm ns umc naucaf naucafñm ñm gfo gfonrnm nrnmafc afcee krgfmc krgfmcrfc rfc

akmvnmafñm qun akmsfgnrcrn`ks vãefgc gurcmtn ne

gkmgn fmtnrvfnmnm gnrfvcgcs gn prf`nr krgnm

rn rnst stk k gn ec umf mfgc gcg g. Ce ns nstu tug gfcr ec na nau uca caffñm

rnspnatk rnspna tk c umc vcrfcien fmgnpnmgfnmtn. fmgnpnmgfnmtn. Nstcs

gfonrnmafce efmnce g gn n krgnm m mk lk`kjæmnc+ ++ ‹‹

naucafkmns, bumtk akm su akmgfafñm fmfafce, sn

+ ‹ + 0 ( ) ( ) ∙∙ c xy c xy c xy c xy c xy jx () () () () ()

pung pungnm nm

() mM m m 3 3 9 34 , supkmgrn`ks qun tkgcs ecs

nm nmak akmt mtrc rcrr

nx nxpr prns nscg cgcs cs

nxpeàaftc.

nm

okr` okr`c c

oumafkmns c x c x cx cx cx m m ( ), ( ), , ( ), ( ), ( ) ∙3 934 y j x( ) skm akmmucs nm um fmtnrvcek ak`òm F y cgn`ãs c x m () 4 ≤ skirn ne `fs`k fmtnrvcek F.

9.3.9 TYKIEN@CQ

9.3.1 WNKYN@C GN N\FQWNMAFC V

Ce fjuce qun nm ne acsk gn ecs naucafkmns gn prf`nr krgnm,, tc`ifæm krgnm tc`ifæm ns prnaf prnafsk sk aunskmcrmks aunskmcrmks canrac gn ecs ak akmg mgfa fafk fkmn mnss gn nxfst nxfstnm nmaf afc c y umfa umfafg fgcg cg qun qun gnin gninm m scsoc sc socanr anrsn sn pcr pcrc c qun ecs ske skeuaf uafkmn kmnss gn prk prkien ien`cs `cs rn rnce cens ns qung qungnm nm if ifnm nm gn gnm mfg fgcs cs,, ns gnaf gnafr, r, gnin gnin`k `kss prnafscr quæ akmgfafkmns gninm au`pefrsn pcrc pnmscr prf`nrk

qun

um

prkien` n`c c

nmn

skeuafñm,

y

pkstnrfkr`nmtn busacr qun gfalc skeuafñm snc òmfac. Ne sfjufn sfjufnmtn mtn tnkrn`c tnkrn`c,, nmumaf nmumafcgk cgk sfm gn`kst gn`kstrca rcafñm fñm,, nstcienan akmgfafkmns pcrc ec nxfstnmafc y umfafgcg gn ec skeuafñm gn um prkien`c gn vcekr fmfafce.

9.3.7 NA^CAFKMNQ GFONYNMAFCENQ EFMNCENQ.

9.3.7.3 TYFMAFTFK GN Q^TNYTKQFAFÑM.

7

   

^mc naucafñm gfonrnmafce efmnce sn gfan qun ns

Ne

lk`k lk`kjæ jæmn mnc c

prfmafpce`nmtn gn ec naucafñm gfonrnmafce efmnce

akmgf akm gfaf afñm ñm22

sf sn Qf

scs scsoc ocan an ec sf sfju jufn fnmt mtn n

{U {Ugf gfsp spec ecys ysty tyen en Uplf Uplf

(x (x)} )}{U {U

prfmafpfk prfmaf pfk

gn

supnrp supnrpksf ksfafñ afñm m sn

kaupc kaupc

lk`kjæmnc. Ne mk`irn gn nstc tnkràc sn `cmnmn

gfspecystyen Uplf (x)} ns umc skeuafñm, skeuafñm, tc`ifæm

csà pkr su

sf`feftug akm ne prfmafp afpfk

gn

ek ns

{Ugfspecys {Ugfspecystyen tyen hU,Uplf hU,Uplf (x)}{Ugfsp (x)}{Ugfspecyst ecystyen yen

supnrpksfafñm cpefacgk nm sfac y ktrcs ãrncs gn ec

hU,Uplff (x)}, gkmgn {Ugfspecysty hU,Upl {Ugfspecystyen en h}h ns umc

afnm afnmaf afc, c, nm ne au auce ce sn ns nstu tugf gfc8 c8 sf nxfs nxfstn tnm m gk gkss ns ns` `ue ueks ks nm um sf sfst stn` n`c c efmn efmnce ce,, nm nmtk tkma mans ns ne

akmstcmtn akmstc mtn criftr criftrcrf crfc c mk muec. muec. Wnmfnm Wnmfnmgk gk nm aunmtc nstc akmgfafñm, acgc tær`fmk nm umc

rnsuetcgk mntk gn su ounrzc nm cejòm `k`nmtk y

naucaf nau cafñm ñm gf gfon onrnm rnmaf afce ce ef efmn mnce ce gn ec vcrf vcrfci cien en

nm cejòm eujcr snrã nqufvcenmtn c ec su`ctkrfc gn

gnpnmgfnmtn y, gnin akmtnmnr y k aucequfnr

ecs ounrzcs ounrzcs gn

gnrfvcgc gn y.

fmgnpnmgfnmtn`nmtn.

Ne Ne wrkmshfcmk ns ne gntnr`fmcmtn gn ec `ctrfz akmstrufgc ce akekacr ecs oumafkmns nm ne prf`nr rnmjeñm (k ec), ec prf`nrc gnrfvcgc gn acgc oumafñm nm ne snjumgk rnmjeñm, y csà lcstc ec au aucg cgrc rcgc gc,,

m-3 -3,,

okr` okr`c cmg mgk k

ceju cejumc mcss

cs csàà

vnan vnanss

gks

ns`ueks ns`ueks

tk`cgks tk`cgks

9.3.? QKE^AFÑM JNNMNYCE GN ECQ NA^CAFKMNQ EFMNCENQ

9.3.> GNTNMGNMAFC N FMGNTNMGNMAFC EFMNCE ZYKMQHFCMK

gnrf nrfvcgc vcgc

nstks

umc

`ctrf ctrfzz

ee eec` c`cg cgc c

`ctr `ctrfz fz

oumgc`nmtce.Nm umc naucafñm gfonrnmafce efmnce gn snjumgk snjumgk krgnm, krgnm, ne wrkmsh wrkmshfcm fcmk k pungn pungn snr aceauecgk pkr ak`putcgkrc `ãs oãafe`nmtn pkr ec fgnmgcg gn Cine.

mk`irn

akekac`ks

sn eks

`cmnmn tær`fmks

csà

pkrqun

sf

qunakmnmnm

ec

oumafñm fmgnmfgc y eks gfonrnmafcens gn ec ouma oumafñ fñmf mfmg mgn nmf mfgc gc nm um ecgk ecgk gn ec nauc naucaf afñm ñm gfonrnmafce, nmtkmans ne ktrk ecgk gnec naucafñm ns fjuce c anrk. Nstk pungn vnrsn aecrc`nmtn nm ec naucafñmgcgc `ãs crrfic. Tkrnstn`kvk, sn en

akmkanak`kl akmkanak`klk`kjæ k`kjæmnc. mnc.

Ec naucafñm naucafñm sn

eec eec`c `c efmnc efmncee pkr pkrqun qun ne gfonrnm gfonrnmafc afcee gn ec ou oumaf mafñm ñm fmgnmfgc y ec oumafñm fmgnmfgc nm sà cpcrnanm skeks y mk okr`cmgk pcrtn gn cejumc ktrc oumafñm ak`penbc.

Ynguaafñm gne krgnm gn umc naucafñm gfonrnmafce efmnce gn snjumgk krgnmc prf`nr krgnm, akmstruaafñm gn umc snjumgc skeuafñm c pcrr gn ktrc yc akmkafgc Ynskevnr umc naucafñm gfonrnmafce gn krgnm nmæsf`k pungn snr, nm kacsfkmns, um pkak

9.3.?.3 YNG^AAFÑM GN KYGNM.

nmjcók nmj cóksc. sc. Nm akmsna akmsnaunm unmafc afc,, snràc snràc `ua `ualk lk `nbkr `nbkr sf tuv tuvfær færc`k c`kss umc naucaf naucafñm ñm gf gfon onrnm rnmaf afce ce ef efmn mnce ce gn prf` prf`nr nr krgnm krgnm k um sf sfst stn` n`c c gn nauc naucaf afkm kmns ns gfonrnmafc gfon rnmafcens ens gn prf`nr krgnm pcrc sustufr ec naucaf naucafñm ñm krgnm nmæsf`k. Nstk

sn pungn lcanr

akm ec cyugc cyugc

efmn efmnce cens ns

gfonrnmafc gfonrnmafcee

gn

gne `ætkgk gn

rnguaafñm. Nxfstnm rnguaafñm. Nxfstnm trns pks nspnaàaks nspnaàaks gn naucaf naucafkmns kmns gfonrnmafc gfonrnmafcens ens gn snjumg snj umgk k krgnm krgnm qun pun pungnm gnm snr rng rnguaf uafgcs gcs cgnauc cgnaucafk afkmns mns gn prf prf`nr `nr krg krgnm2 nm2 3. Naucafñm gfonrnmafce gn snjumgk krgnm qun mk pksnc vcrfcien gnpnmgfnmtn.

>