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# WS4Key - i{an g lf Math 224 Spring 2007 Quiz Worksheet 4...

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Unformatted text preview: i {an g lf/ Math 224, Spring 2007, Quiz / Worksheet 4 Name: ' M” ‘k i Use the front and back of this Sheet to complete the following problems. If additional paper is needed, staple the extra Sheet to this one. Consider the system of linear differential equations gig-[— w AY Y(O): ( 8:3: > ”x W M Sill?) " Diff : ED? w fly ‘) l/(Jrl n (W .(a) Write the system (*) {fl/11* “2T2 in matrix form ‘le l“ 8 l W \$2:~-~m11+ 4:132 f: \/(f):: \Rk Q ﬁ)t‘ lilﬁﬁ *» l ) (Q , xx M 3m l 32476” M awn we no i i; { l 3/“ 24; ﬁt) l WM “L “E :3 we» % « il ‘4 alt?» l ll V l W l t ”C; 21% It é” “HOV A“ ”AW (0 N 6%)) ‘4! a “EA/y r: (f) "r a? a l. <4; WW 3 a l \7( 3 :11; < l \\ N ( Ll (fl l” le 2- Ll lK; l” Ll i ”L t, l i “I; > t "M ”F . _, ' ~ l W m r a a l: w . l, 2 (a) For the initial condition Y(0 )2 < 1 , ﬁnd the particular solution of (*) 5- le w m» g l .M , , M L m l.- \( ta 5M5; l “.5 Eta L3 at l i 53 WW?” the» M“? "Jr tea l at: W (H ill (1)) Sketch trajectories through this; initial condition both in the phase plane and in the solution plane. On the phase plane, also indicate straight line solutions from W prohlem 1. l// XL» \Rﬂll‘) . M V2 Q‘WMyMMWNW ...
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