Assignment 3

Assignment 3 - AM351 Spring 08 Due Friday, July 18 2008...

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AM351 Spring 08 Due Friday, July 18 2008 Assignment 3 Instructions: write your solutions clearly, explain your steps carefully and refer to the- orems and lemmas when needed. The assignment is due either in class or in the as- signments drop box (4th floor) by 2pm. 1. ( 3 marks ) Consider the following inhomogeneous equation y 00 + xy = e - x . (a) Show that 0 is an ordinary point of the equation (b) Find the general solution of the equation in terms of a series about 0. (You only need find the terms up to x 6 ) (c) In your solution to part (b) identify the parts of the solution, i.e. y h ( x ) (the general solution of the associated homogeneous equation) and y p ( x ) (a particular solution of the inhomogeneous equation) 2. ( 3 marks ) Consider the equation xy 00 - y 0 + 4 x 3 y = 0 (a) Show that 0 is a regular singular point of the equation. (b) Find two linearly independent solutions of the equation. (c) Express your solution in terms of known functions.
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Assignment 3 - AM351 Spring 08 Due Friday, July 18 2008...

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