final_22b_07

final_22b_07 - Ordinary Differential Equations Math...

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Unformatted text preview: Ordinary Differential Equations Math 22B-002, Spring 2007 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 ): y + 2 ty = e- t 2 , y (0) = y . (b) For what initial-value y is y (2) = 0? 2 2. [20 pts.] (a) Solve the initial value problem yy + 1 = t, y (6) = 3 . (b) For what t-interval is the solution defined? 3 3. [20 pts.] (a) Find the equilibrium solutions of the equation y = y ( y- 2) 3 . (b) Sketch the phase line of the equation, and determine the stability of the equilibria you found in (a). (c) How does the solution with y (0) =- 1 behave as t + ? How does the solution with y (0) = 1 behave as t - ?...
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final_22b_07 - Ordinary Differential Equations Math...

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