Assignment 3

# Assignment 3 - AM351 Spring 08 Due Friday Assignment 3...

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 07/28/2009 for the course AMATH 351 taught by Professor Sivabalsivaloganathan during the Spring '08 term at Waterloo.

### Page1 / 3

Assignment 3 - AM351 Spring 08 Due Friday Assignment 3...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online