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BUT RRR : w y=) a(x = ¥0)" n=0 PABA HERR Bp . ay _ Exl isa txy=0 Solution : wo See ye poe as dd & ony? E Catone se? | {ra=m) e2. 3 a~ \. 8 SO: & 2B ®cmem SRG, C1 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: FexeB renlor stigdlar petit, 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 tT=0 2 3H OO VZ AL Sigs’ Indical eqpotion + ” aa [ht Sram? 4.3 BR BBR BHERBORRRS ARMADA : 1. REARH, (Bessel Equation } d?y dy 2a 4 2_y2)y=0; ge ttt & v*)y=0;veER Cy RE A AE BR (Bessel Function) : = . Cp" A. 2ntv Iy= ercreranie n=0 Ge ee Jv =) Te GS)” accor: 1)°2 pbb Ux EA, row) RRAREAR ACRAH RACLAPER roan RR 2. RBA RHA (Legendre Equation ) d? ad a = x2) 3 = x + n(n t Dy = O;neN PUM Ms oe EA A a a: d”™ P,(x) syle? - 1") ~ Dini dx” RAG A MA BAX, (Legendre Polynomial) > 2443 7aH = RT CaS S OAR s Gono Function re (pe at ME : POe)= XTC) Ponys-d) Chev) 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: LIF} = (Pee Sat afetsrty |S as fo sr tn eat 2 “Ht 3455 “tot BWAR: SL Hen} = SP F)- (SOI IO+4 ) $5) BLA RAF ODE FF > FT 298 AG HX, Laplace Transform #2 7% Inverse Laplace Transform ¢ Ex2 : 2 4 3y = 13sin(2t); y(0) = 6 Solution : Li si39} = $¥(s)- Ble) + 3¥ts) Af isanaty 19 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) Ans: Foto cs(xt) +3an Gt) SOBRE BA? Ong Gri Qs (+ God = Rt) > ars 4 any Sly + + God Yis) ~ QCs)= FO) 2h) Sate - -- Syn)» s"9F o> 5 megerd ai x i Ola. .- 2. py Oo x re ’ 5.3 £249 Dt me ARS 1. Lfe“f(.)} = F(s— a) 2. LEf(t — ayu(t — a)} = e~F(s) Qe): neu = (5) | cg (= Ok PHRA) Proof : Ss oO Meet =f pane Eat = €* FG) ~Ltrea js F(S-a) 7° 0 ebay ut-a) one = SO peo) Etat . Sct-0) Sled op atten) Ex3! a+ y=fOs yO) =5; fO= {scos(ty; eu Solution : se” - Ais: erre-5- Fe Gr) YQ - OO) Fi 8) Se 2G #7 sien ae): \ ae) = db)eS =ert e” = (StYCs)~S= FOI =i ed ‘3 | Sct) 308t Ut-h) = 3es[t Oy uct) = oti 436” (
