quiz 2 - i-> +or-..:. . \ <. y...

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Fall 2008 Math 285 Quiz 2: Sep 17 Name: If you cannot complete a problem (perhaps because you forgot a formula) but you think you know how, please describe. Correct methods will receive partial credits. 1. The figure below is a computer-generated direction field that goes with the differential equation y' = 1 - xy. Add to the figure an approximate solution curve for the IVP dy dx = 1 - xy, y (2) = 1. ~ C6\.vv <A C. v r-v--L ~ ro l~ L~ ~O,V\ -c l'--I l) ~v -l~, L~ CUj\. .-AZ I) 't~(\T '"to l~ aIr-rowS (\V-.J\n,. 2. Consider the autonomous first-order differential equation y' = f(y) where the graph of f is given below. Use the graph to locate the equilibrium (critical) points, and sketch a phase portrait. S ,V\ U- :) 1= 1( lj) ~ 0 Vv~ Y -=- -( ~ 'j~~~ I ~,Q\\ ~ -l a~1j7'- f< 0 ·~O~ Y <. -l~SQ lj « 0 .-rl~.
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Unformatted text preview: i-&gt; +or-..:. . \ &lt;. y &lt;:&quot;Z. So ~ ( &gt; D '\:~ I Classify each equilibrium (critical) point as asymptotically stable, unstable, or semi-stable.---- I : s MUll SL. .o\~lP.-'.-~. ~\ Q 5 .~\\ (\ &lt;. r0Q.9) ~ \ vv L~ lj IS '\ ~d. .. \(~ l:~ ..... 1 o-d ~ &amp;.Lcr. . Q9,J-e. ~. .-v~ I.j fS ': &gt;&quot; ~ ,&gt;~U)Iw-l~-I ; ~.-e. . :J ('A\)~\ q~'l-tlb/V\ ~:::-I '2 l S 0...(\ ~ S~ .A1.~ . 5~~~ ~ ~+ .5 ~ 14. .0~ ~ T ~creJ. \ 'j ~ L 3. Solve the given differential equation by separation of variables. What's an explicit solution? d.-j ::J ~\l~' = ~ r- .JUx. n.l; t', l' ' I \ ::&gt;0\&quot; ,...
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