Math 232, Test 1, January 25, 2005 Name: Instructions. Do 8 of the following 9 questions. Each is worth 5 points. 1. Consider the following system of dierential equations modeling a predator-prey system. dx x = .5x 1 + .3xy dt 2000 dy y = .7y 1 1.2xy dt 1
Math 232, Test 2, 12 February 2005 Name: Instructions. Do any 7 of the following 8 questions. Please show all of your work. Good Luck! dy dx = x + 10xy and = 3y xy. 1. (4 pts) Consider the predator-prey system of equations dt dt Find all equilbrium points
Math 232, Test 3, 7 March 2006 Name: Instructions. Do each of the following six problems. Please do your best, and show all appropriate details in your solutions. Thank you! 1. (a) Find the general solution to dY = dt 2 1 -1 4 Y.
(b) Find the specific sol
Math 232, Final Test, 15 March 2005 Name: Instructions. Do any ve of the rst six questions, and any ve of the last six questions. Please do your best, and show all appropriate details in your solutions. Thank you! dy y y 1. Draw the phase line for the die
Math 232, Test 1, January 25, 2005 Name: Instructions. Do 8 of the following 9 questions. Each is worth 5 points. 1. Consider the following system of dierential equations modeling a predator-prey system. dx x = .5x 1 + .3xy dt 2000 dy y = .7y 1 1.2xy dt 1
Math 232, Test 3, 1 March 2005 Name: Hints and Answers
Instructions. Do each of the following ve problems. Please do your best, and show all appropriate details in your solutions. Thank you! 1. (a) Find the general solution to the linear system of dierent
Math 232, Test 1, 30 January 2003 Name: Answers and Hints 1. Solve by separation of variables. Thus, y= dy = y2
t2 2
(t + 2)dt, and so y 1 =
t2 + 2t + C, or 2
1 . + 2t + C
Now, y(0) = 1 implies C = 1, so the solution to the initial value problem is y=
t2
Math 232, 23 January 2004, Exam I Name: Instructions. Please do your best and show all appropriate work in doing each of the following eight questions. 1. (5 pts) Consider the following system of dierential equations modeling a predator-prey system. x2 dx