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math 310 a5 - MATH 310 Differential Equations Homework...

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MATH 310 Summer 2011 Differential Equations Homework Exercises, Set 5 Quiz on Wednesday, 19 October 2011 Course Information is on WebCT Textbook references are to: Boyce and DiPrima Elementary Differential Equations and Boundary Value Problems ” (9th edition). Reading : Sections 2.4, 2.5, 2.6 Problems to prepare for quiz (no need to hand in): Section 2.4, # 6, 12, 15, 21, 22 Existence and uniqueness, interval of existence Section 2.5, # 3, 7, 10, 12, 13 Critical points and stability, qualitative behaviour In each case, also determine lim t →∞ y ( t ) if y (0) = 1 . 5 , without solving the differential equation Section 2.5, # 18 Recall: the volume of a cone of base radius a , height h is 1 3 πa 2 h . Section 2.5, # 20, 23 Applications to fisheries management and epidemiology Section 2.5, # 26 An introduction to dynamical systems and bifurcation; you should first read the preceding text beginning at “ Bifurcation Points and read (or try) #25 Section 2.6, # 4, 6, 13, 16, 18 Exact equations First rewrite #6 in the form of an exact DE (note that this DE is homogeneous)
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