final_22b_sample_07

final_22b_sample_07 - Ordinary Differential Equations Math...

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Unformatted text preview: Ordinary Differential Equations Math 22B-002, Spring 2007 Sample Final Exam NAME.................................................................... SIGNATURE.......................................................... I.D. NUMBER....................................................... No books, notes, or calculators. Show all your work Question Points Score 1 20 2 20 3 20 4 20 5 20 6 20 7 20 8 20 9 20 10 20 Total 200 1 1. [20 pts.] (a) Solve the following initial value problem for y ( t ) in t > 0: y- 2 t y = t, y (1) = 2 . (b) How does y ( t ) behave as t → + ? 2 2. [20 pts.] (a) Solve the initial value problem y + (cos t ) y 2 = 0 , y (0) = y , where y is an arbitrary constant. (b) For what values of the initial data y is your solution defined for all-∞ < t < + ∞ ? 3 3. [20 pts.] Consider the ordinary differential equation y = ( y- 3) ( y 2- 1 ) (a) Sketch a graph of the right-hand side of this equation as a function of y , and find all equilibrium solutions of the equation....
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This note was uploaded on 03/05/2009 for the course MATH 22B taught by Professor Hunter during the Spring '08 term at UC Davis.

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final_22b_sample_07 - Ordinary Differential Equations Math...

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