08SpringHwk03 - Math 3301 Homework Set 3 10 Points Modeling...

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Unformatted text preview: Math 3301 Homework Set 3 10 Points Modeling, Part II For these problems you MUST set up and solve the appropriate IVP(s) in order to receive any credit for the problem. Any decimals must be to at least the 4th decimal place. 1. A population of mice in a field grows at a rate proportional to its population. There are originally 75 mice in the field and in the absence of any outside factors the population will double in 2 months time (assume 4 weeks/month). Initially, each week there is a net migration of 5 mice in the lake and predators eat 10 mice. After 5 weeks net migration increases to 8 mice/week and the predators still eat 10 mice. How many fish are there really after 2 months time? 2. An 10 kg object is dropped off a bridge with a downward velocity of 2 m/s. The air resistance experienced by the object is given by 6v. If the object hits the lake below 10 seconds after it was dropped how high above the lake was the bridge? 3. Let's go back to #2. Once the object hits the lake the "air resistance" increases to 10v. If the lake is 50 meters deep at the point where the mass hits and it falls straight down what is the velocity of the object when it hits the bottom of the lake? Equilibrium Solutions Find and classify the equilibrium solutions for each of the following differential equations. 4. y = ( y - 1) e 5. y = 3 y 2 + by 3 , 4+ 2 y b < 0 Euler's Method 6. Find the approximate value of the solution to the following IVP at t = 1.4 using both h = 0.2 and h = 0.1 . All decimal work should be to at least the 4th decimal place. y + t sin ( y ) = y 2 y (1) = 3 ...
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