practice-exam1-427K

practice-exam1-427K - M427 K PRACTICE EXAM 1 Directions:...

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Unformatted text preview: M427 K PRACTICE EXAM 1 Directions: This exam is meant to suggest the kind, di culty, and number of problems on the real exam. Note that topics covered in the course, but not included on this practice exam, still might appear on the real exam. Set aside 50 minutes during which you can work on this exam without interruption. Refer to no books, notes, or calculators while working on the exam. This will give you a sense of your level of preparation for the real exam. 1.(20pts) Solve the I.V.P. (3x2 2xy + 2) + (6y 2 x2 + 3) dy = 0, dx y (0) = 5. 2.(20pts) Using 0 = 0, find the next two Picard iterates (using the method of successive approximation) for the I.V.P. y 0 = 2t(1 + y ), y (0) = 0. 3.(20pts) Solve the I.V.P. y 00 + 9y = 0, y (0) = 1, y 0 (0) = 0. 4.(20pts) Find the general solution of y 00 + 4y 0 5 y = e 2t . 5.(20pts) The equation ty 00 (t + 1)y 0 + y = 0, t > 0 has the solution y1 = et . Find a fundamental set of solutions. 1 ...
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This note was uploaded on 11/28/2011 for the course MATH 427K taught by Professor Delallave during the Fall '11 term at University of Texas.

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