Math 245 Ch3 TestSolns_Fall08

Math 245 Ch3 - Fall2008 Math 245 3 Chapter T est(3 D ecember008 2 Name So,U"Mattr^ l C lass i ty tne i J(t A =l p r o b.l C o n si d e rth e

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Fall2008 Math 245 Chapter 3 Test (3 December 2008) So(.,U" Mattr^ Name: (t l\ prob. l. Considerthesystem x'=Ax wherethematrixAisgivenby A=l; iJ. Classitytne fixed point x = 0 of the system as to its stability and type' r^1 I C,'*{.,,;h n' ugnwu^ (A, ad(a-fr)= [ ;^ t^'.\ =O 6r-x,)"- 4=-o t*, = 12 {> 1-= r!2 =-/. B \rt** L U^s,t.,h!o r ( * g,{tw!,! )^ Fg}Ax3Q,n t) F"uA tt D a ltAfu , Cu6ul-ut oru \opfooli ct") prob.2. Find the general solution x(l; = Cl,x(t)(l; +{:rx@(t) of the second-order system x'= Ax where the matrix A is given ^ " = [i ,t) &tc^^xrr) = | t;t ,-1 il = (3-x)64) +4 = f- qt+z+ t:o 'tr { t-' tr \ t''4L+1 =6')"=o fu=1,2 (p+'nL
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I= f)= I $ D.[n^l^l ttt ttanr.**. ql i[=l1,r({) eI t vc) &.hcft - tfu oXn- v% (1) L q\ 2t =V g 3-1. -1 rr 4v,d)\ lfl 0t l=o + 4 t-zl\q J vo)_ Vlt =_ o kdLC 9wu ila t y^*t "n Pst"ltlt\n6'rualt'6 oF et [email protected]"t) = Vto)be'" * *'1"d " Sr}gt.fun r;b x'=/A( - "tt(.{+xt) t'* e7tr: 4xrn'tezt @, Ivat-Auct) 6r + A\to
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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 Ch3 - Fall2008 Math 245 3 Chapter T est(3 D ecember008 2 Name So,U"Mattr^ l C lass i ty tne i J(t A =l p r o b.l C o n si d e rth e

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