MATH 212 Homework Assignment 1 Solutions, Fall 2016

American University of Beirut · Introductory Partial Differential Equations · 4 pages · with solution

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MATH 212 Homework Assignment 1 Solutions, Fall 2016, page 1

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ia Mat Az Assghmat 4 6 (aud)- Ab - AMG) -4.42- 4-47- A.al~ 4-28 Carb, 0) iy IDs “a 4 U, = cde Uge -e% sin ‘ a i a a . x SDUrrr Uzy = O Ary Yan = eo wry, U yy = eo cory x | a) w CH 4S 3 Wr Bay Be ik ~t Ux = Baby Ugo 6x , d s =, mae + = LX. Use = 6X uyg 2 6X > Uy = O - ay Ww ao Log O% A y = (Re \ £09005 4 i Uz, e aX igen ER. x a 3 ae Wee = BOM -8xGx) 2% uyy = 20a) 244). 20% 99 C+ ty AYU Otey ny G sete ye Ox 43) z D> Unxttlys =O _ Wage w= or) » re as t | = *FOQ UL = UL TY, = Cr): cos Rae wee VR Ixy "gy T 5’ Ge) + = Lé (r ‘\ Oerg®) “3 ce) = Se IO + Se yg CMY KAS y 8 ‘ Hire aay fOr) 7 gl V IF u = Uper ra 55>) o Vutege Uy 2 28D + se fed > Cty) PO + orp FO NX (x ey) a _ => ay A + fe $F” (d= Ua + Yay = Pee” Ft => { oa dt = ( ar SHON ENS Cia = Iv'Gal = +28 => LiGd= ‘a, by Girt. oR => LOS = an asl ' en by Aes. whi = 6 4y bien a> Gt t a 4 bh. Up = Cr + AoE + 3X’ Uy = eis. IG hace t - ' Ure = Ady Une = Roy Ups Use =D Cgaty ae w Ctyx > = Cot oc, t+ cr X +. Se, CHA) + cat k DL Lethon ete Ad a eet Gente 1 But Ute = UKeé bi He itn se eee, a Tw => Utctr=Uew 2 A% ve) Moe Vr =U. and Ug Yat => Une = Vee fy y Ue = Vae Une = ew a) by At Uy, = Uwe 4 nice ine Sr er IEhE = SO r { Uni Sa eS Vi Cb Dd= Ua Ctr D by aa veto thew of callers Nousver, Vx CU xD = F'Gd+ Li Lie CspoS alee = fede? (t ug Gadts f'Od+ cee Cea ie CO, x) (Ue wot pitt hy. CD, hs fil = up (dx) fa / Tit fos LOS = Ue CGsrd¢ s v Ctx d= (* uy (cds * , reo Sti (sox Sd 2 Jf AAF- a- home Law Fle ponbhearn Z b- mewknrar - e- Keme Ln —" e- home ba & - ehkome Lin Adl- o- WS fle Alhl+ CK Ves. EC'HD, ype 5, d, Ceflscuny)] Ve ir, £EG'LDS Py b- LLfrf, l= LOZWLEA Ve -daad<o d=0 LEefj=seLl¥] Ve Gi, £ ECC) a i Ov arb e ase seniea ak aba > A. QQ a- UW’ + Aus lt ceox AS. wk) = VOd+ de , how V(X) is th. sol of Vitdveo Uuxoa ory Ve Iie 6 od Wale £,|voea)<q -axte vids be™ ae= Ae Bsr +G 4% de’ = Qisox - Caw = Buex- CA + 2A + BBX 4+ AGeex = |+uw => 2h=t- 7 , b+ 8G) g AB-G=0 Oat °° B=! - 2620 * oe c= w&rd= bis Oa 4 ery ae 2 CO7KXx gi / : 5 “2 - se’ = SGUe= Dcéex i pe hee ee ee eee ie. St ~ “el 2 eg =e eo _ c=-l rede os 10 UOd = Cpe +e * Yo X ig 5 c- ULYSs VES = “v9-t@v’ eiov co Ine *-1 Pew 410 = © ve 9 zl-1} ae = A + e Cbibo x4 Ceenm) Ap’ = eX Crore Conn) + Berne C wx) Np” = eX CBee + C52 ~ Bere Creo») ter G foawx + Crerx — taco x - C5Xx) = oC-QRenx+ QCwx ) e*CeABadx Pr ae ee -\ Ve CBhoxs Corn — Poccx + Ge tio + LO e* CO bor + Caen) — (4+ Xemx Ayo —-1#E 12 B-1E 4108 = | ~VCR=aI | Ba-Yo ~19% -19¢ +1¢ +10G =O an (S) bE (a0. mz Cc “a t ; x : x jer coo tx + Qe Antx +4, — 4, efoox 7