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# P1spring09 pages 1 - Prelim 1 Math 2930 show work 6 problems no calculators Spring 2009 1a(4 points Write your name and section number at the top

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Prelim 1 Math 2930 Spring 2009 show work, 6 problems, no calculators 1a) (4 points) Write your name and section number at the top of this page. 1b) (10 points) Solve the diﬀerential equation y ± + 1 5 y = e - t for y ( t ) having initial value y (0) = 5. 1c) (6 points) (1c is not related to 1b) Find a function f ( x, y ) so that the exact equation 2 x 2 ydx + 2 3 x 3 dy = 0 says df = 0. 1

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2) (16 points) A virus infects a population of 10000 individuals as follows. Let x ( t ) be the number of infected, which we model as a diﬀerentiable function. The rate at which x is increasing is proportional to the product of the number of infected and the number of uninfected. Initially 50 are infected and the rate when x = 250 is 25 per month. Write the diﬀerential equation for x ( t ). Find the equilibrium solutions and determine their stability. You are not asked to solve the equation. 2
3) (16 points) Consider the second order diﬀerential equation y ±± = - y 3 with initial conditions y (0) = 0, and

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## This note was uploaded on 01/21/2011 for the course MATH 2930 taught by Professor Terrell,r during the Spring '07 term at Cornell University (Engineering School).

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P1spring09 pages 1 - Prelim 1 Math 2930 show work 6 problems no calculators Spring 2009 1a(4 points Write your name and section number at the top

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