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# A1 - professor plays video games The next day 500 sudents...

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NAME Assignment 1 DUE: Jan. 25, 2011 (In Class) MAP 2302 001 Please show all your work. The answers without solutions will not be graded. 1. Solve each of the ordinary differential equation explicitly: (a) dy dx = 1 1 - x solution goes through P = (2 , 1). (b) dy dx = - p 1 - y 2 solution goes through P = (0 , 0). 2. Determine the following for the solution dy dx = 1 x 2 . (a) Monotonicity (b) Concavity (c) Symmetry (d) Singularities 3. Sketch the isoclines for the following O.D.E’s (a) dy dx = x 2 + y 2 for k = 1 , 4 , 9. (b) dy dx = x 3 for k = - 8 , - 1 , 0 , 1 , 8. 4. Santa Fe College has about 17,000 students enrolled in the Spring 2011 semester. On the first day of the Spring Semester, a class of 40 students heard their differential equation
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Unformatted text preview: professor plays video games. The next day, 500 sudents had heard this rumor. If the rumor spreads according to the logistic equation y = ay ( b-y ), where y is the number of students who have heard the rumor, at what time will 95% of the students be aware of the rumor? [Note: 0% of the students care about this rumor.] 5. Determine whether Existence-Uniqueness Theorem implies that the given intial value problem has a unique solution. Explain. [Do NOT solve.] (a) dy dx = y 4-x 4 and y (0) = 7. (b) dy dx = 3 x-3 √ y-1 and y (2) = 1....
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