In each question, draw the phase diagram (i.e. the graph with stationary points and arrows), determine the stationary points, and classify each one as stable, unstable or seminstable (by considering the sign of the derivative of the right-hand side). 1. i = -x + 1 2. i = 2x – x² 3. i = -x(1+x)(2 – x) 4. i = x? – x4 5. i = x²(4 – x²)

Solve the differential equation xdy - ydx = 2x³dx. A. y = x² + Cx B. y = x³ + C C. y = x³ + Cx D. y = x² + Cx³

. Wildlife biologists are studying the fish population of a lake which is stocked with a specific number of fish every year. They discover that the fish population, P (in thousands), is well-nodeled by a differential equation, where t represents time, in years. A slope field for this differential equation is shown to the right. The wildlife biologists are interested in understanding how the fish population will behave based on various starting populations and have hired you as a mathematical consultant. Write a report to the biologists that specifically addresses the following questions: 10// 8. イ ブブ / ブ/ノ/// 4 71/1 ブ ブノ ィ イ • What, if any, starting populations lead to a die off? • What, if any, starting populations lead to a population explosion to infinity? • What, if any, starting populations lead to a stabilizing of the population? 24ーーイイイイ 1. 1/////// 1/// /////////////////// /// 2 4 6. 8. Make sure to indicate why and how you reached each conclusion based on the slope field. Your…