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(aeELH) tes: 2a? 2 Ex2: x — Ay = x%e* ax Solution : BB 4 (Bld = xe” - of - 7 OR a al a0 gasxt WL obx 2 tS Xd) = Xt tne Slax] = nt (xe ec) aK: 2 ge CO ae text Bb pays -% (unolefinedl) 1, OB ARR a 1 Ex3:2= dx x+y? Ans: REX ext Solution : Bia bien Pema ABAD: 5g = PX 9 B-x- of (FEMS) - * (eo Pag MOs= et cP , Pile?) aoa ay ee aod ope cbse) = -Fapasce? 2 Pets fadetad = ge -afgdte*) 2 Heb agotra[e'98 = fet oge* ae*ic fips: Paparce’ex 2.3 RRB 1, FRRA COKER WH RAMIEM EA CAZHK) f(x y)dx + g(x y)dy = 0; f(tx,ty) = t’ f(x, y)(same as g) MIS Dek = Ua d= Wd XA > Fovd= hci) 5 gierd)= X"GU4) 2) SCM) dx + FLW) Cuolxr xed) =d [SCM UGC A)) 20 = ~ BU) oh CARI! ) 2. @¥4] 4 HX (Bernoulli’s Equation ) d & + P@y = fay" dx WS ee VEG 5 oh o en ou). ryt ds 3 th chess uh. Seoul =e >| rap 2 (by) Sts Pus $0) REY) rokaa ta 3. & = f(ax + By +) fash: Set UA Barc 9 He AL BAR 2 38-89 BB org GED Wek : SHA HX, (Exact Equation ) HRA 24 £Y 92 _oa- ag 8x Exl : 7-102 425 =0; &4u-fte Solution = er rm ‘O25 @ x (& ery olX = OSE nem ax 5 EXC hax = nit) e% CNB CO) > ne” Ans AKe™ 3.2 PRR RA BIER) d"y q7t On Fen + Gp-1 mt +... +49y = 0; dy € constant. giae. « nREB RIMM RA -| JAX, 2 Ones Ong mer -- +e" © > Cain rai 4 Gozo CANE Aristh) SE A BIAAS Comiltogy equation ) 3 (m-AD AD“ Cm-Aa)= 0 Rte ABLAZE ly AKGIR -SERAR aes tK + RCM oi) AGC) SPEAR OD BR LR fer Re ARE Cee eee wel ? Bere BOA) 22% (cus ext eX) / © Casta LIN) Ex2: <4 25% “ty =O Solution : 4: mint +9 aqntlye° Dm=t LGB) Age CORK COMIX G KEBXT GMX ts: Clas It CXOSH A CEKENX 3.3 RRB d’y d™ty Qn Fyn + Any Det +... +agy = f(x); a, € constant. fe hi netgobr * ; Pal) Prog SN Sods pat ke Ke PD Acos(wt) + Bsin(mt) Hesyst+ B’sntet. Pr(xde™* Prooe™ Pn (x)cos (wt) Prec coat Pr Ox ke* cos (wt) Ke cas uta ke Smet, Tike Pa(xje“cos(wt) Pk eas ack: + PROC Enact, *Y=VetYpy go2.2 SPU BI RAA RD AI RAGA ona? alage=o HAAR BIA -£8.20 BER G8 —+Oade FO Gaga 4 Gofp> 400 ttt AS LB 2 Bl6| 1% Sop= Dae LHR 1 OR HSR BEL ap renee BAO ) 3.5 #8-KRFA#E (Cauchy-Euler Equation ) BETABGE-F BEEMERERAR EI GM SI n nol yx" me + yx at +...+d9y = 0; ay € constant. MR? be B= x 3 Oa mor) omens)" + QoX"S0 2 OntRy! * Oona meni 10070. (ImAREAREAA Gy aay Saga, eR Mom) amiet)) 3 On Ad(n-A2- + N-An) =O M Ax eR AEE Cb | ot sng SPiscipied RABE LK di Ape € 4 ., a Met, der ot Bi sted th SHAK ARB ARYp 2 elo (PiaXD+ sin (8.00% YJ FE. Teas (@eanc) - aon (609) 9X05 (6 600, Xml Chin) axg 2 _ yaya Exd x0 oa Gt = In@) enon mt |=0 ope A [ban ol + re oe tmOn-) - = > m~amt| 20 5. etal Soeur hx > m=| B48) =f Melle) = §- bent) soe Gra split = AE toe A= \t asi" % ee oe | Laxtl tx Re Aiz [2° doe Yoel" EX = = Me 24 4G AR Ana 33° (reap ¥Ct) +A ee) ax % fl = bx = CXC Xba Xt 2 “re. » fie Ans: Crean alt oD, 3.6 FREBERD A Be LB EAT ax tdvertt ie a tT e= () dx dy thy X= Coszte Gonat+ At 7rg ) Dit bys 0 a , 4: a poayeaye tt MEM eats gh JeCarCycosats Cganat +75 qt 3 9 GK Aa OIA 2 ae cee tire 5 42-4 3 Xe: Cuebat+ Gonz Xp: flor Kee ALE BL IC. 4 , n= Goss Smt + E+) SOAs AAP ett tes , Ars: 92 Gt Layesrtt-de-Gyanat, 4 dtd gt 4. RRA Ate HRe Re 4.1 FPR BR RAT SARA > BUT RRR : w y=) a(x = ¥0)" n=0 PABA HERR Bp . ay _ Exl isa txy=0 Solution : wo See ye poe as dd & ogni E Coa one R? {ra=m) e2. 3 a~ \. 8 SO: & So emem BRG,C ae gyO Gag 1 aaa Selma GerOrtl) +n X= 0 73 aa ™ 2G esa Cs" TEER 2. C20 Gn Ct EPOAD Gans hac” Ceaae Ck 2 Ces Ee 2) Cant{s aE" 42 TA oe ee = eee + -H)3k son FRB: Ars: d= Gog, Thais) 2 4 Cot CX aro 42y= HOR BANTER E 3x d*y 1dy 1 dx? * 3x dx 3x7 ° DAVE BLA FL xO RRP BK > 12 BR EE ER Bl PRL AE ee: Frobenius’ Theorem GLA : d"y Prax —x%q)d™ ty Po(X— Xo) 0 dx” (x —X%9) dx™t ~ (L= XxX) HPA (X — Xq) BRAM > ASH — AR: Faxes regalo stagdlar peiitt, y = > nes 7 Xr n=0 Ex2: 3x52 42_y=0 Solution : yood GanBh2) =Cr-1 pe 2 tne rats? Cre Co nix % 59 Calg) NEC ' call 2 Coe by Ge Co coh wp ap nt 4L(k2) fe & Zoo yr-} | ox Gd = on - Facrowniwry) x BY oe Loe \ “Bs 8 ont Cn eX) el, 2. BCovtr-}+ Cot xl z= [enonved (ansrn) - Crt 1 ~s Go¥0 if 1 + arte Nt ted 2 37D D0 V3 AL Sigs’ Indical eqpotion + ” aa [ht Sram? 43 BRBBR BHRRGARMERS AWAD : 1. REARH, (Bessel Equation } 2 2 Yas oe —v*)y=0;vER EW a ARES 37 AR A RE BR (Bessel Function) : x2 = . ie 1)" REV =) orn ro to yen n= be = aire ® He RE, A pov) BRAREAR BoRAH RALHARP FR a POV RRAREA 2. RA HX (Legendre Equation ) d? d 2) 2 4 nent Dy = 0; neN APF Ho Oe EOF Re: 1 a” 2 7h Pel den Oe" — D"I RAG A MA BAX, (Legendre Polynomial) > 2443 7aH = P(X) = ET CMPHS OAR Sy Gomme. Function re (pe at MG : Pos)= XTC, | Poms)! Che) 5. Laplace Transform BAR MBRAA > RAL GA S| 5.1 £& LiF aF eyo =| "feat = F(s); s€C 0 6 30. 8244 Laplace Transform : f@® F(s) 1 1 _ s t” uae s eat - + - . k sin(kt) Paw s cos(kt) roar] 7 k sinh(kt) woe sz s cosh(kt) Vue Proof : es =-¢ te" hoe io Weed St 1 2g" S45 a Sey ' 2. LPTs wa ‘ge a Aen é i Hob. 7 dea n ME Bt a Laplace Transform : ee: LLP eI} = (Pee Sat afetsrty |S as fo sr tn eat 2 “Ht 3455 “tot BRAK: . rege cr) ; BLA RAF ODE FF > FT 298 AG HX, Laplace Transform #2 7% Inverse Laplace Transform ¢ Ex2 : 2 +4 3y = 13sin(2t) ; (0) =6 Solution : Li si39} = $¥(s)- Ble) + 3¥ts) Af isanaty EFRS? &) Lf (SHIGID seo SH Is*o 4+ ac B-F- $246 8 $ 65S gg Gre) s3- aqls| » B-2-$.-3.8 Bo Yeo D8 2 StS aah = BS cacostat)43oniat) 19 Aus: Foto cs(xt) +3qn 0%) EE BF And Gn OS /- + Gog = Rt) | Yis)- Q(s)= FCs) | Ee, Pw SE ~~ Sy) 2 SaMap smn Qt): : 7 a” 0). ght 3b) a cs coe peng © NOTE K 5 2 ee) 5.3 £92 F - 1. Lhe" f(O} = F(s— a) 2. Lif (t— aju(t — a)} =e F(s) Bau = (9) oy (C= OF BATA) Proof : SP gaye “ON yp =f" gO. EM at! = €* Fs) = Leta ee}. Fts-a) 2. ite £660) ult-a) ot ab = SO $66.0) Mat SP §cb0) ES ct Bx3: 2+ y= f(t); (0) =5; f = [scascey; feo Solution : ase” a StUYS)=5- “Fee Grp YQ- BS Fis) sé a= ¥- ation ge): 1 Mo) «gees GINS) ~S= FO GE Jet) = Bost Weir) = BesTe TOI A) = 1ge" (Si BTR 2) Fed: 3 2 Lf asttwo} oyor 523 Earn) . 36 eS an ty - Rust uct) fins 66% Suc [e Lastest] 
