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Unformatted text preview: AMATH 351 Assignment No. 3 Fall 2005 Due: Friday, October 7, 2005, 1:30 p.m.. (You can slide it under my door if I am not in my office.) Unless otherwise indicated, all power series solutions are to be about the point x = 0. In each question, justify the type of power series solution being assumed by indicating the nature of the point x = 0 in the DE, i.e., ordinary vs. singular, regular singular vs. irregular singular. 1. Find two linearly independent series solutions to Airy’s DE, y ′′ + xy = 0 , (1) for x ≥ 0. Write explicitly the first three nonzero terms of each series. You do not have to determine the general form of the coefficients. What do you expect to be the radius of convergence of the series? Why? 2. Find two linearly indpendent series solutions to the DE, 4 xy ′′ + 2 y ′ + y = 0 , (2) for x ≥ 0. Write explicitly the first three nonzero terms of each series. You do not have to determine the general form of the coefficients....
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This note was uploaded on 09/20/2010 for the course AMATH 351 taught by Professor Sivabalsivaloganathan during the Spring '08 term at Waterloo.
- Spring '08