MAT 127: Calculus C, Fall 2009Mini-Quiz:qualitative properties of 1st-order differential equationsDO NOT TURN THIS PAGE OVER YETThis mini-quiz 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 dia-grams of solution curves and direction fields; for one of them you will need the textb ook. A problemon 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 6-9minutes for the first problem before starting on the second and do not look at the first problemafter that.Taking about 20 minutes on the analogous problem on the final should be ok (this would be onepoint per minute, which is what you need to average). Thus, you are being asked to complete themini-quiz at about 2.5 times the pace needed for the final exam; this is because you do not have 7other problems to deal with and are under less pressure. However, please do not rush through theanalogous problem on the final.Problem AConsider 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:Iyx11IIyx11IIIyx11IVyx11Match each of the diagrams to the corresponding differential equation (the match is one-to-one)and explain your reasoning:diagram I II III IVequationProblem B: 7.2 3-6,
View Full Document
Unlocking...