09SpringHwk02 - Math 3301 Homework Set 2 10 Points...

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Math 3301 Homework Set 2 10 Points 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 4 th decimal place and you may need computational aids in finding some of the intervals of validity. Separable Differential Equations 1. ( ) 2 5 0 1 8 3 x y y y ′ = = + 2. ( ) 3 0 8 7 8 y y y x x = = + 3. Solve the following differential equation and determine the minimum value(s) of the solution. Any approximate answers must be to at least the 4 th decimal place. You may assume that 0 y > . ( ) ( ) 2 1 0 3 x y y x x y ′ = = e 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 4 th decimal place. Modeling, Part I 4. A 1000 gallon tank contains 800 gallons of water with 45 ounces of dye dissolved in it. Water with a dye concentration of ( ) 100 10 2 t c t = e ounces/gal is flowing into the tank at a rate of 6 gallons/min and a well mixed solution flows out at a rate of 6 gallons/min.
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