MATH 212 Homework Assignment 3 Solutions, Fall 2016

American University of Beirut · Introductory Partial Differential Equations · 3 pages · with solution

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MATH 212 Homework Assignment 3 Solutions, Fall 2016, page 1

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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) |