MATH 212 Homework Assignment 1 Solutions, Fall 2016
American University of Beirut · Introductory Partial Differential Equations · 4 pages · with solution
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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