Math 245 Ch4 TestSolns_Fall08

# Math 245 Ch4 TestSolns_Fall08 - Fall2008 M ath 2 45 4...

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Math 245 Chapter 4 Test (15 October 2008) Name S"eJ*i^ Moi6, Prob. 1. Find the general solution of the 2nd-order ODE + - 4+ + 4y = 4s z' clt' dt c,hono"tzrlsl.c \$n, yL 4r+ 4 = n&,r ts= l, Y-= 2, Gzf= o Lt , ^Lt 6" r t e--,rf r C*y.D,t "ft) l\$crt5l"cxra Sn{L. \$* rtl = ct ezt * crt tb. !rnc. tfu v,o" -4m,ngl^!4nt6^l^ a ha^hc.r{d^ slLrf6^ +.rl- &.*, S"!-hl"*c ;*1 K oDE: G,l,^l^/ 9t!,.*h,: \$ru= H+,/+l+Ylt) \' = qtb rc^b m"L uar,or.,a*t: W ho-Lfua Y= A a': y! - 2A62+; Y4= AAe'r Y "* 4Y'+4Y: A{ 4- 4(-2) 43 d'"' A 14 rs+ 4t d'*= ,^!i7* ^- 4.=L ,.\_ lL_4, Fall2008

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prob. 2. The characteristic equation for a 3'd-order ODE is given by (t +2)(r2 +4r +8) = 0. Write the real-valued solution of the homogeneous ODE and sketch the location of the characteristic roots in the complex r-plane. C)a^*bilsfut radh Y+2=o YT4t+g=o + + *.[, -1r4{6 a .u f =^2. r--4tYa'-4-ai'' u- :L-= -2!.21 -1f grtl= Cre- + 0 -rf ee + -1b =ee + Gr-ti) f qe *ca At'+J xt I Kcl;ztl V tr C, e(-'*IDt* ui"{e."* a"{ K cre \$*t
Prob. 3. Find the particular solution of the 2nd-order ODE t4+9y:4sin3r ' 1T*- c-N'^orfiil"e{i. \$vt ,rar \"?9 =o + tr'= t 3i LJeHo, f.f^rr^"{-tt* EaArl^ 'it H*B = q ar3s+ Qedib' 0"e +4t /"cr4 t" ron^**. [ook- !* "'t4"1]c,rl4^c{*h *f, {*", YCg- [ f s,Ds 3h Y'= A{ c63t -3te;G4

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## This note was uploaded on 11/08/2009 for the course MATH 245 at USC.

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Math 245 Ch4 TestSolns_Fall08 - Fall2008 M ath 2 45 4...

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