Exam 1 ReviewMAP 2302Disclaimer:This review is by no means complete.Please study the homework as well as the lecturenotes. These questions are just an outline of the material.1. Chapter 1 KNOW: definition of differential equation, difference between explicit and implicit so-lution, initial value conditions, how to sketch a graph, isocline, given a direction field sketch theapproximate solution.(a) Solvedydx= ln(x) withP= (1,1).(b) Letdydx=r2πsin(x2). Where is the solution monotonic? What symmetry (if any) doesy(x)have?2. Chapter 2 KNOW: autonomous first order differential equation, equilibrium solutions, stable, unsta-ble and semistable solutions, phase line, Existence-Uniqueness theorem, applications like MalthusModels (simple exponential growth), and Logistic Models.(a) Determine the behavior of the equilibria fordydx=y(y-1)2.(b) Letdydx=y1/3through the point (0,0). What does the Existence-Uniqueness theorem state?
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