MATH 212 Homework Assignment 3 Solutions, Fall 2016
American University of Beirut · Introductory Partial Differential Equations · 3 pages · with solution
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oo NATH Ur,
Aasigrment 3 fp
2-44— 2.4.3- 2.4.4 Gove) —-24.b -— WG.N Carb) -
HY Ca). -
ay \- wbp-= JL Flowetd +$-eP Jor, J g (5) ds
acl
ky. - ; wv hane. Fo oe a a eee pinning axel
ty -&- =) roe § oe ot
=> wl ee fia ee +d ( _—
a-ct ect
—O+rc)* ~ Ge-et)* me
a ce [ é x te ] ~4- coo A oT
oly
~ = Gceeky® -G-cth*
aU ea ee
2-4.3- U,lo,x = ft ye ted = 4)
AC a
= u CO, =O cs ga) ig
UCox~Ss=F LEO FG-t) } + ‘aa yeu
a-t
qfsdds = if “gledde
c ant
art
~4£ Loro\ +4 f
a-
an~F 1 ankbxtt < |
: t
=> uCtyx< £ ‘~ ods=<o
at-&
woh x-E C1 and Adart <Q .
a+
=> uctyxd< aff Ods +f 4s | et[mt-)
+ iff x-E Si ond xrE er _ =
; ‘ .
=> uv Ctad= 4 f Odst { ds *s ods| eglaijeL
xe ‘
* if x~-t > 2 and x+ ber
if x-E > 1 anck ae
2.44. ay cexxupt = |
g
—
xe
|
oO
= u Ctya*>= ae J.
ods \
=> u(t» =e | pr ds ‘|= + [xrt- ate b
a-&
uctsx>= 4 $ Get 1) x-ESV L 1 <xrtS 2
" x-E<\ > XttS2@
An
£0a-* +b) z>x-to!s xtb> 29
is x-E oly x+b<z@
O ejfthanissmes ‘)
cos (xt &) + 6 (x-t)
bys cee lx Bree ha = Pee re a
U Cx S= ©
Up (O,xS=kerAan
~t [ = Se
= x te a t Pas Ce
a a°s = 4 -Z
=> w CO,;x) = OF gle>
(0.x) = dxv = ge)
Up et xe
2 =
uw (xt = = ¥ as” ds a re
4 ed, 3xtt+ KE
afro? ~ 0 a Aan Zi= ax Jt
> + axt
=
i Vet Pa
Re x >= Sox)
Vxx = Uxx Ct-te,a)
See Utet Ctyxd=o” Ure Ctx) WEd0
Hpin Urp Cite »xD>=c% Un Ct-te,x) vt>t.
Vee =H Vx
SevGAa>~ ult-torx» is a sol te Vy<ct¥e VOt,
a VCto,x dz u Cth-b, x) -—ul0d, x>= £&) +
Ve Cty x= Uy Cte ~*~ y= Ue Cox» = 9,6) (. ‘
ra (cD = Atwk
— GOD= er ® meat
aCtpd= 4 LFA + Pa-an) +4 § Adds
: -At
—_ti|{Aw~ (x+ ab) , Aw (x-2t) | t pai, neat
2 L t a
[sn Gxr b+ Aw - 24) ) - | Arba 20) ed) |