Ordinary Diff Eq Exam Review Solutions 1

Ordinary Diff Eq Exam Review Solutions 1 - 1 Solutions...

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Unformatted text preview: 1 Solutions Section 1.1 1. The rate of change in the population is the derivative . The Malthusian Growth Law states that the rate of change in the population is proportional to . Thus , where is the proportionality constant. Without reference to the variable, the differential equation becomes 2. a. This statement mathematically is where we have used to represent the proportionality constant. b. This statement translates as where we have used to represent the proportionality constant. c. The overall growth rate is . Thus the Logistic Growth Law is 3. Torricelli’s law states that the change in height, the square root of the height, . Thus proportionality constant. is proportional to , where is the 4. The highest order derivative is is . so the order is and the standard form 5. The highest order derivative is . so the order is . The standard form is 6. The highest order derivative is is . so the order is 1 and the standard form ...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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