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Unformatted text preview: MAT 127: Calculus C
MiniQuiz:
qualitative properties of 1storder diﬀerential equations DO NOT TURN THIS PAGE OVER YET This miniquiz is for practice only. It will not be graded or even collected. On the next page, you will ﬁnd two matching problems involving diﬀerential equations and diagrams of solution curves and direction ﬁelds; for one of them you will need the textbook. A problem
on the ﬁnal exam will contain two diagrams of each type for matching with 4 diﬀerential equations,
thus being a mixture of the two problems on the next page. You have 15 minutes to complete both problems (not each!) on the next page. Please take 69
minutes for the ﬁrst problem before starting on the second and do not look at the ﬁrst problem
after that. Taking about 10 minutes on the analogous problem on the ﬁnal should be ok (this would be one
point per minute, which is what you need to average). Thus, you are being asked to complete
the miniquiz slightly faster than needed for the ﬁnal exam; this is because you do not have other
problems to deal with and are under less pressure. However, please do not rush through the
analogous problem on the ﬁnal. Problem A
Consider the four diﬀerential equations for y = y (x):
(a) y ′ = 2 − y, (b) y ′ = x(2 − y ), (c) y ′ = x + y − 1 (d) y ′ = sin x sin y. Each of the four diagrams below shows three solution curves for one of these equations:
y
I y
II 1 1 1 1 x x y
III y
IV 1 1 1 1 x x Match each of the diagrams to the corresponding diﬀerential equation (the match is onetoone)
and explain your reasoning: diagram I II III equation Problem B: 7.2 36, p506 IV ...
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 Fall '07
 GuanYuShi
 Differential Equations, Calculus, Equations, 15 minutes, 10 minutes, 9 minutes

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