Unformatted text preview: Math 3301 Homework Set 2 10 Points Separable Differential Equations For problems 1 & 2 find the solution to the given IVP and determine the interval of validity for the solution. Any approximate answers must be to at least the 4th decimal place and you may need computational aids in finding some of the intervals of validity. 1. y = ( 6 x - 3 ) e 2 + y 2. y ( 0 ) = -2 y = y2 9 x - 16
2 y (1) = 1 13 3. Solve the following differential equation, find the interval of validity for the solution and determine the minimum value of the solution. Any approximate answers must be to at least the 4th decimal place. y = 3x - 1 5- 4y y ( 0 ) = -2 Modeling, Part I For problems 4 & 5 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. 4. A 100 gallon tank contains 70 gallons of water with 4 ounces of salt dissolved in it. Salt water with a concentration of c ( t ) = 3 - 2 e
20 ounces/gal is flowing into the tank at a rate of 7 gallons/min and a well mixed solution flows out at a rate of 7 gallons/min. If left to forever, what would be the equilibrium (i.e. what would be the amount of salt in the tank as t ) amount of salt in the water? 5. A 1000 liter tank initial contains 500 liters of water with 20 grams of contaminate dissolved in it. Contaminated water with a concentration of 8 grams/liter flows into the tank at a rate of 2 liters/hr and a well mixed solution flows out at a rate of 4 liters/hr. This will continue until the concentration of the contaminate is 200 grams. At that point in time the concentration of the incoming of contaminated water is decreased to 2 grams/liter (flow rate remains the same) and a well mixed solution flows out at a decreased rate of 2 liters/hr. Home much of the contaminate is in the tank 2 hours after concentration of the inflow is changed? 6. Take the same situation from #5 and after that 2 hours is up the inflow of the contaminated water is shut off and pure water is pumped into the system at a rate of 6 liters/hr while the rate at which a well mixed solution flows out stays at 2 liters/hr. Set up, but do not solve, an IVP for this new situation. ...
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