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1b-2009-exam_3_practice

# 1b-2009-exam_3_practice - growth model then solve it Show...

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Math 1B — Exam #3 Practice Fall Program for Freshmen 2009 Fred Bourgoin 1. Use Euler’s method with step size 0.1 to estimate y (0 . 3), where y is the solution to the initial-value problem y 0 = x + xy , y (0) = 1. 2. A tank contains 20 kg of salt dissolved in 5000 L of water. Brine that contains 0.03 kg of salt per liter of water enters the tank at a rate of 25 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt remains in the tank after half an hour? 3. The initial size of a population is 100. After 2 days, the population size has increased to 300. 1. Give the differential equation for a natural growth model, then solve it. Show your steps. 2. Assuming a carrying capacity of 5000, give the differential equation for a logistic
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Unformatted text preview: growth model, then solve it. Show your steps. 3. Solve x 2 y + 2 xy = cos 2 x . 4. Solve y 00-4 y = xe x + cos 2 x . 5. Solve y 00 + y = tan x . 6. Use power series to solve ( x-3) y + 2 y = 0. 7. Solve 4 y 00 + 12 y + 9 y = xe-3 2 x . 8. A spring has a mass of 2 kg and has damping constant 14, and a force of 6 N is required to keep the spring stretched 0.5 m beyond is natural length. The spring is stretched 1 m beyond its natural length and released with zero velocity. (a) Find the position of the mass at time t . (b) What mass would produce critical damping? (c) What damping constant would produce critical damping?...
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