PersamaanDiferensial Biasa

7/23/2019 PersamaanDiferensial Biasa

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EMXBEMXG@M VB@MWMSM GXS | =

IM@RLXMS XB@OALADG @BLMRXMO

KRVRSMO XB@OG@ ^BV@M^MLMO @mepus GXS Suàlgla, Surmfmym 9>===

Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6

Bemgl ; `mpmlNgts/mc/gh

Caroblgus Xaoy Sutbkm *8==>=>>>23'

^brsmemmo Hgibrbosgml Fgmsm

M/ Xuruomo ^mrsgml

^mohmod iuodsg / Xuruomo pmrsgml hmrg tbrjmhmp *hbodmo ebemohmod àostmo

hgtulgs

Xuruomo pmrsgml pbrtmem hmrg tbrjmhmp *hbodmo ebemohmod àostmo' hgtulgs ;

Caotaj ;

Xuruomo pmrsgml tgod`mt `bhum ;

Caotaj ;

=/

6/ Xmepm` fmjwm ;

Mtmu

Kg`m em`m hgsbfut hgibrbosgml tatml hmrg

¶

¶

mailto:[email protected]






EMXBEMXG@M VB@MWMSM GXS | 6



Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



Albj `mrbom gtu kg`m hgfbrg`mo em`m hghmpmt fmjwm;

F/ Hbigogsg ; ^H mhmlmj sbfumj pbrsmemmo ymod ebrupm`mo jufuodmo motmrm turuomo *hbrgvmtgi

hmrg smtu vmrgmfbl tm` fbfms tbrjmhmp smtu!lbfgj vmrgmfbl fbfms/

Xgod`mt hmo hbrmkmt hmrg sumtu ^H

Kg`m turuomo tbrtgoddg ymod tbrhmpmt hmlme pbrsmemmo mhmlmj tgod`mt o, em`m ^H gtu hgsbfut ^

tgod`mt o/

Kg`m pbrsmemmo gtu sblurujoym rmsgaoml hmo fulmt hmlme turuomo%turuomo gtu, em`m pmod`mt hm

turuomo tbrtgoddg hmlme pbrsmemmo gtu hgsbfut hbrmkmt ^H gtu/

Caotaj ;

=/ ^H t` =, hbrmkmt =

6/ ^H t` 6, hbrmkmt =

3/ ^H t` =, hbrmkmt 6

^H

^H Fgmsm * ^HF'

Wmod ebodmohuodjmoym smtu vmrgmfblfbfms/

^H ^mrsgml * ̂ H^ '

Wmod ebodmohuod lbfgjhmrg smtu vmrgmfbl fbfms/

Caotaj ;

=/

¶

6/

Caotaj ;

=/¶

6/










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



^H hmrg fbr`ms ùrvm hmtmr

Hgfbrg`mo fbr`ms ùrvm hmtmr ; …………………………………………………………/*='

Hgtmoym`mo ^H fbr`ms gtu/

Cmrmoym sff ;

^brs/ *=' hgturuo`mo tbrjmhmp ; /…………………………………………………………/*6'

Blgegomsg hmrg *=', *6' hghmpmt jufuodmo motmrm ;

Caotaj ; Hgtmoym`mo ^H hmrg fbr`ms dmrgs lurus ………………… *='

^boybl/ ; Hgturuo`mo tbrjmhmp ; ………………… *6'

Blgegomsg hmrg *=' hmo *6' hg hmpmt ^H ymod hgtmoym`mo gmlmj ;

^boyblbsmgmo ^H ;

Mhmlmj sumtu iuodsg tmopm turuomo%turuomo hmo ebeboujg ^H gtu/

^boyblbsmgmo Reue ̂ brsmemmo Hgibrbosgml *^R^H'

Mhmlmj pboyblbsmgmo ^H ymod ebeumt àostmotm%àostmotm sbfmrmod ymod fmoymòym smem hbodm

tgod`mt hmrg ^H gtu/

^boyblbsmgmo ̂ mrtgùlgr ̂ brsmemmo Hgibrbosgml *^^^H'

Mhmlmj pboyblbsmgmo ^H ymod hghmpmt hmrg ^R^H kg`m pmhm àostmotm%àostmotm sbfmrmodoym hgfb

oglmg tbrtbotu/

Caotaj%caotaj ;

Gog ebrupm`mo ^H imrg fbr`ms *='










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



=/ ^H

hgtulgs

^R^H ;

6/ ^mhm sbtgmp tgtg` hmrg sumtu fbr`ms ùrvm hmtmr hg`btmjug fmjwm àbigsgbo mrmj dmrgs sgodduodoy

mhmlmj 6 `mlg mfsgsoym/ Xbotu`mo pbrs/ ùrvm hmtmr gtu ymod eblmlug /

^boybl/ ;

^H

^R^H ;

Eblmlug tgtg`

Kmhg pbrs/ùrvm ymod eblmlug *=,6' mhmlmj ;

C/ ^H tgod`mt smtu hbrmkmt smtu

Fbotu` ueueoym ; mtmu

=/' ^H hbodmo vmrgmfbl%vmrgmfbl tbrpgsmj

Fbotu` ueue 0

^R^H ; ∠ ∠

Caotaj ;

¶ Gog ^R^H










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



Sblbsmg`mo ^H ;

^boybl/ ; ∠ ∠

^R^H ;

6/' ^H hbodmo vmrgmfbl%vmrgmfbl ymod hmpmt hgpgsmj`mo

Fbotu` ueue ;

^R^H ;

∠ ∠ Caotaj ;

Sblbsmg`mo ^H ;

^R^H ;

3/' ^H Jaeadgo

^H 0 hgsbfut ^H jaeadgo kg`m hmpmt hgtulgs hmlme fbotu` ;

Sufst ;

Caotaj ;

Sblbsmg`mo ^H

;










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



Kg`m

Kmwmf ; ^R^H

8/' ^H fbrfbotu`

=/ Kg`m Sufst ;

Ebokmhg ^H hbodmo vmrgmfbl%vmrgmfbl tbrpgsmj/

6/ Kg`m Sufst ;

Hgemom {

Em`m ^H ebokmhg ^H jaeadgo ;

Caotaj ; Sblbsmg`mo ^H ;

^boybl/ ;

sufst ;

^H ebokmhg ; jaeadgo

Lmlu egsml`mo ;

Hst/ Hghmpmt ;

^R^H ;

2/' ^H B`sm`

^H 0 b`sm`

^R^H b`sm` fbrfbotu` ; ……………………………………/*='

3










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



Fbrmrtg ; ∠

……………………………………/*6'

Emu hgcmrg P∠ U ……………………………………/*3'

Em`m hghmpmt ^R^H b`sm` ; ……………………………………/*8'

Caotaj ;

Sblbsmg`mo ^H ;

^boybl/ ;

@mrbom Kmhg ^H b`sm`/

^R^H b`sm` fbrfbotu`

^R^H 5

9/' Im`tar ^bodgotbdrml

^H 0 XGHM@ B@SM@ …………/…………………………/*='

Hgsblbsmg`mo, `btbeu

Emsu` *6'

¶







EMXBEMXG@M VB@MWMSM GXS | :



Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



Kg`m mhm Y sbhbeg`gmo jgoddm ; EBOKMHG B@SM@ ……………………………………/*6'

Em`m Y hgsbfut im`tar pbodgotbdrml hmrg ^H *='/

m/ Kg`m Y5i*x' smkm/

Em`m ;

Sbjgoddm ;

∠

Caotaj ;

Sblbsmg`mo ^H ;

^boybl/ ;

∠

^H ; b`sm`










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



^R^H ; gmlmj ;

f/ Kg`m Y5i*y' smkm,

∠







EMXBEMXG@M VB@MWMSM GXS | =>



Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



Caotaj ;

Sblbsmg`mo ^H ;

^boybl/ ;

∠

Hmo sbtbrusoym hghmpmt ;

^R^H ;

4/' ^H lgobmr tgod`mt smtu

Fbotu` Reue ;

……………………//*='

i/p/ *Im`tar ^bodgotbdrml' ; ∠ ……………………//*6'

hgemom ^ hmo ] mhmlmj iuodsg tbrjmhmp x/

^R^H ; ∠ ……………………//*3'

Caotaj ;

Sblbsmg`mo ^H ;

^boybl/ ; i/p/

∠

^R^H ;

:/' ^H FBVOARLLG







EMXBEMXG@M VB@MWMSM GXS | ==



Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



Fbotu` Reue ;

; …………………//*='

Sufst ;

^H ebokmhg ;

Caotaj ;

Sblbsmg`mo^H;

^boybl/ ;

Sufst/

3 3

^H ebokmhg ; 3

Hst/ Hghmpmt ^R^H ; 7/' ^H VGCCMXG

………………………//*='

Kg`m àostmo ∠

Kg`m

Kg`m

¶







EMXBEMXG@M VB@MWMSM GXS | =6



Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



Ebohmpmt`mo pboybl/ Reue ^H Vgccmtg sff ;

Hgcmrg ! hg`btmjug pboybl/ pmrtgùlmr

Em`m ; ………………………//*6'

Mefgl

Caotaj ;

Sblbsmg`mo ^H ; Kg`m hg`btmjug pboybl/ ^mrtgùlmr /

ml/ ;

Em`m pboybl/ ^H Vgccmtg tsf/ mhmlmj ;

¶

^H Fbroaullg










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



SAML%SAML LMXGJMO^H HBODMO ^BRFMJ%^BRFMJ XBV^GSMJ!HM^MX HG^GSMJ@MO

HM^MX@MO ^BOWBLBSMGMO RERE ^H ;

=/

6/

3/ 3

HM^MX@MO ^BOWBLBSMGMO ^MVXG@RLMV ^H ;

8/

2/

SAML%SAML LMXGJMO

^H JAEADGO

9/

4/ 3 3

:/ 3¶

SAML%SAML LMXGJMO

^H FBVFBOXR@

7/

=>/ 33










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



==/

SAML%SAML LMXGJMO

^H B@SM@

SBLBSMG@MO ^H FBVG@RX ;

=6/

=3/

=8/ 3










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



SAML%SAML LMXGJMO

IM@XAV ^BODGOXBDVMLMOHM^MX@MO IM@XAV ^BODGOXBDVMLMO HMVG EMSGOD%EMSGOD ^H FBVG@RX HMO @BERHGMO

SBLBSMG@MO ^H GXR ;

=2/

=9/

SAML%SAML LMXGJMO

^H FBVOARLLG

SBLBSMG@MO ^H;

=4/ 33

=:/ ¶

SAML%SAML LMXGJMO

^H VGCCMXG 0 ¶

SBLBSMG@MO ^H;

=7/

6>/ ¶










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



H/ ^H tgod`mt hum

^H ;


^boybl/ ; ∠ ∠

^R^H ;

Egsml ;

^H ebokmhg ;

Mtmu ;

∛ ∠

∛ ∠

Caotaj ;

Sblbsmg`mo ^H ;

^boybl/ ;

∛

¶

¶

¶¶










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



∛

^R^H ;

| ∛

|

SAML%SAML LMXGJMO

SBLBSMG@MO ^H ;

=/

6/

¶¶







EMXBEMXG@M VB@MWMSM GXS | =:



Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



B/ ^H ………………………………//*='

0 p hmo q àostmo/

ebeboujg ^H gog kg`m ;

@mrbom , em`m hg hmpmt ;

^brs/ @mrm`tbrgstg` *^@' ; …/……// *6' hbodmo m`mr %m`mr hmo /

Mhm 3 `msus ;

Kg`m *rbml fbrlmgomo', em`m ^R^H *=' ;

Caotaj ; ^H

^@ ; ^R^H ;

Kg`m

*rbml `befmr5`', em`m ^R^H *=' ;

Caotaj ; ^H

^@ ; ^R^H ;

Kg`m

Caotaj ; ^H

^@ ; ^R^H ;

¶ >

@aeplb`s kahaj, em`m ^R^H *=' ;










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



SAML%SAML LMXGJMO

FBOXR@ ;

HM^MX@MO ^BOWBLBSMGMO RERE ^H ;

=/

6/ ¶¶

¶¶







EMXBEMXG@M VB@MWMSM GXS | 6>



Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



I/ ^H ………………………//*='

0 p hmo q àostmotm%àostmotm/

*^L 5 ^H lbod`mp'

^H tbrbhu`sg *^V' ; ………………………//*6'

^R^L 5 ^R^H *=' ; ………………………//*3'

5 iuodsg àeplbebotbr *IC' 5 ^R^V *6' 5 gotbdrml pmrtgculmr *G^' hmrg *=' 5 pboyblbsmgmo ymod tghm` ebodmohuod àostmot

sbfmrmod hmrg ^H gtu

Ebohmpmt`mo gotbdrml pmrtgculmr hbodmo ebtahb vmrgmsg pmrmebtbr/

^H ; *='

^V ; *6'

Kg`m ^R^V *^boyblbsmgmo Reue ^brsmemmo Xbrbhu`sg!iuodsg caeplbebotbr' mhmlmj ; ………………/ *3'

Em`m ………………/ *8'

Hgemom

hmo

hgcmrg hmrg ;

………………/ *2'

Caotaj 0

Sblbsmg`mo ̂ H ;

^boyblbsmgmo ;

, hgemom

hmo

hgcmrg hmrg “

Hghmpmt ; ∠







EMXBEMXG@M VB@MWMSM GXS | 6=



Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



Em`m

Kmhg ^R^H ;

^brlumsmo ;

^L ;

^V ;

IC ;

G^ ;

Hgemom jmrus ebeboujg symrmt!hgcmrg hmrg ;

………………………………

………………………………

Caotaj ;

Sblbsmg`mo ^H ; 3

^boyblbsmgmo ;

IC ; 3

G^ ;

3

3 hgcmrg hmrg ; 3 3 3










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



3 3

3 3 3 3 3

3

Em`m ^R^H 3

D/ Apbrmtar H apbrmtar hbrgvmtgvb/

Govbrs apbrmtar H/

Hbigogsg ;

0 e 5 àostmo

^H ; ebokmhg ;

^H ; ebokmhg ;* '

âlgoaegml hmlme H hgtulgs I*H'










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



SGIMX%SGIMX ;

=

6

3

8

2

9

4

Godmt Hbrbt Emclmurgo

= 3

6 3

^brjmtg`mo fmjwm ;

=/' Vueus Bulbr ;

Em`m ; *'

6/' hgbxpmosg`mo ebourut hbrbt ùmsm hmlme H sff/ ;

J/ Ebohmpmt`mo Gotbdrml ^mrtgùlmr *G^' ;

^H ; Sbcmrm sgefalgs










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



G/ Kg`m

palgoaegml hbrmkmt

hmlme

Caotaj ;

Sblbsmg`mo ^H ;

^boyblbsmgmo ; ^V 0 Sufst/

^@ ;

IC ;

GI ;

}

^R^H

GG/ Kg`m

Caotaj = ; Sblbsmg`mo ̂ H ;

^boyblbsmgmo ;

IC ;

G^ ;

^R^H ;

Caotaj 6; Sblbsmg`mo ̂ H ;

^boyblbsmgmo ;

IC ;

DMDML










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



G^ ;

Cmrmoym pm`mg rueus ;

Hbodmo ebemsmod

^R^H 0

GGG/ Kg`m

Caotaj = ; Sblbsmg`mo ̂ H ;

^boyblbsmgmo ;

IC ;

¶

¶

G^ ; 3

^R^H ; 3

Caotaj 6 ; Sblbsmg`mo ̂ H ;










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



^boyblbsmgmo ;

}

^R^H ;

SAML%SAML LMXGJMO

FBOXR@ ;

SBLBSMG@MO ^H FBVG@RX ;

=/

6/

3/ ⁈

8/

2/ G/ ^H BRLBV

Fbotu` Reue ;

Hgemom ;

mhmlmj àostmotm%àostmotm/

Sufst/ ;

DMDML










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



33 3 3 33 3 3 33

Kg`m

3 3

Sbjgoddm ^H hgmtms ebokmhg ;

Gmlmj ^H lgobmr hbodmo àbigsgbo àostmo/

@jusus ;

……………………………//*='

Hgemom àostmotm%àostmotm/

Sufst/ ;

^H *=' ebokmhg ; ……………………………//*6'


^boyblbsmgmo ; Hbodmo sufst/ sbpbrtg hgmtms, ^H ebokmhg ; mtmu ;

^V ;







EMXBEMXG@M VB@MWMSM GXS | 6:



Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



Sufst/ ;

^@ ; IC ;

G^ ;

^R^H / Dmotg hmo

K/

^H Sbrbotm` *^H Sgeultmo'^H Sbrbotm` hbodmo hum pbrsmemmo hmo hbodmo hum fumj iuodsg%iuodsg ymod fblue hg`btmju

fbrfbotu` sff/ ;

Hgemom mhmlmj palgoaegml hmlme H hbodmo àbigsgbo%àbigsgbo àostmo/

^H ebokmhg ; hmo

Fmoymòym àostmotm%àostmotm sbfmrmod pmhm ^R^H sbrbotm` mhmlmj smem hbodmo pmod`mt tbrtgodd

hmrg H hmlme /










Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6



Caotaj ; Sblbsmg`mo ̂ H sbrbotm` ;

^boyblbsmgmo ;

¶

¶

3 …………/ *3'

3

Rotu` sbebotmrm ; 3 …………/ *8'

Hgemom 3 hmo emsgj hmo jmrus

hgoymtm`mo

hmo

/

*3' hmo *8' emsu` *=' 0

} 3 }

Omotg ^R^H sbrbotm` jmoym ebeumt 6àostmotm sbfmrmod smkm/ *









Xblp ; >3= 278 4628, Imx ; >3= 279 8=:6


Hg hmpmt ; 3 3

Kmhg ^R^H sbrbotm` ;

3

SAML%SAML LMXGJMO

^H SGERLXMO

SBLBSMG@MO ^H SGERLXMO FBVG@RX 0

=/

6/





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