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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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 Spring '08
 SivabalSivaloganathan

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