Math204LectureNotesCourseNotes, Lecture notes of Mathematics

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• Sections 5.2 and 5.

Sections 5.2 and 5.3 Aneorem. VThe general solution of He hor OVE Pla)" te Qe). 9” + R).-4 =O Con le. esatken OY oO pore” Denes cente-ed ok US y= 2 ow Goa aa In) provided Snot ‘OY ond R/p are orotate mk Re. “Towler Senedd expansin o+ Xe Wet Rac. Po NY) oreoyar, the =R.0.C. of the power sees Selatin 7 ot leost mind Bac. (%; Ks Dac R%ix)} Examples (1) Any {ie theorem, +o C4) 4 4 3x y! + Ivy =O (4) Roe oO 2S. >. ot X92 O ) Cb) for Ow P S. &. et XK = Ya. . 1 S\ce Q YY = ee ond &p - - a One toone?. 2 unckhons ) oad SM ce x+h #O On (— oo, ) ) these Dunchons mre nol ye en Cw 00). Therefore , bu ea alone «= Kom » Mee qerenl salcton of 4+MWAS ODE con be vont (eo) os o BS. ab wed , ond OW) ad aw PS. ok rele Ca), ee Second park ap ro theo , the 2.0.C. ? hig Powe Sene) Soluhton ak Ko=O vs ot (esst min] 20.C, 3 50) Roc. (45 yy =x (o) Sul , we 2.0.¢. oP da OVS. sshittln of xQe MO, 1S ot eost min} 20.0. (Bi 3%.) XO... © ))) = ee St — “% he a y+ mx) 4/ + (cosx) 4 = O at Xo= O. Previous ly » We observed hast \yothh She ed wy oe owlatie ot % = O worth Roc ( sx ; 0) = ROC (eos x 3 0) = Co. Therefore by Shu alo ove srneun , Se grok Solution af. ws ONG cri ik wala aS w& power Benes at K=O volte AO.C iy CO. (3) Fad tu VS. solution dy - Oe 0 w/t Kad ot x =O. L Aly Van +htorntin, we ~ mumedio: see ~thok the genecal soli COW be vwatlean as o& owes Sane) at YX vs} RVC. co .] wt\ co “ -\ == Nn For = x” - N-&.- K = 2. Qt) Oana, X eee 8k TG) toes ® oo “ co y= 2. a(a-t) Ay or = 2_@+2) Cre \) Qnner x oo “ 2 co 9S aod AED - QO "Lee ©) +4) = 0 h=7Z h=1 a n=O ~ A) A So Vv we VW 7 3(ut2) Grtl) ogg — Dinan e™ +7 Vem 42 Four” = O A-09 n= ( "n=O vaio fear ovr ey t 2_| Cura) atl) omen = On + GH) aney 4 wen | x" = O n= | =0 = 0 - n=1,2,3, ..- _ —KUja ~ Cua) Ont \ Onay = & nx\ uvzl,r 30... wae & Caner) Cutt i (W-&) 3 Cn42)Cutt)