Chapter 5
Series Solutions
So far we have given a systematic procedure for constructing fundamental solutions only if the equation
had constant coecients. There is no known type of second order, linea
MATHEMATICS 3161: Fall 2013
Assignment # 3 (Due Date: Oct. 21)
1. Transform the given equation or initial value problem into a system of rst order equations
or a system of rst order equations with ini
AMATH 3161,
Midterm Exam,
Name:
Fall 2007
Student No.:
Instruction: This exam includes 5 questions. All answers must be carefully justied. The value of each problem is marked on the left margin.
[25]
S o lu t io n t o H W 5 ( A M A T H 3 1 6 1 )
X
3
=
1
2
2
2 2
1
=
2
0 . T h e n 1 2
e ig e n v e c t o r . In t h e s im ila r w a y , fo r r
to
2
H e n c e
2
2 r
0 a n d w e g e t r
2 , s u p p
MATHEMATICS 3161: Fall 2013
Assignment # 1 (Due Date: Sept. 23)
1. Determine the radius of convergence of the given power series.
a)
n=1
(2x + 1)n
n2
b)
n=1
(x x0 )n
n
2. Rewrite the given expression
MATHEMATICS 3161: Fall 2013
Assignment # 5 (Due Date: Nov. 29)
1. Consider the initial value problem
y = ty,
y (0) = 1 ,
hand-calculate the rst ve iterations of Eulers method, the rst three iterations
MATHEMATICS 3161:
Fall 2013
Midterm Exam (Oct. 18, 2013)
n 1 n 2
n+1
1n
n+1 n
1n 1
1
(
x
+
x=
x+
x= +
+ 2 ) xn
2
2
3 n=1 n + 3 n
n=2 n + 1
n=1 n
n=0 n + 3
n=1 n
1. Sol:
5x
, x = 0 is not a singular po
MATHEMATICS 3161: Fall 2013
Assignment # 4 (Due Date: Nov. 8)
5
2e3t
, y2 ( t ) =
are known to be solutions of the homogeneous
1
e3t
linear system y = Ay , where A is a real 2 2 constant matrix,
a) Ve
MATHEMATICS 3161: Fall 2013
Assignment # 3 (Due Date: Oct. 21)
1. Transform the given equation or initial value problem into a system of rst order equations
or a system of rst order equations with ini
MATHEMATICS 3161: Fall 2013
Assignment # 2 (Due Date: Oct. 4)
1. Find all singular points of the given equation and determine whether each one is regular or
irregular.
a) (1 x2 )2 y + x(1 x)y + (1 + x
Memorial University of Newfoundland
Applied Mathematics 3161: Ordinary Dierential Equations II (2013.9-2013.12)
Course web-site: www.math.mun.ca/ yyuan/math3161.html
Course Outline
Slots: Lecture 09
C
MATHEMATICS 3161: Fall 2013
Assignment # 1 (Due Date: Sept. 23)
1. Determine the radius of convergence of the given power series.
a)
n=1
(2x + 1)n
n2
n=1
b)
(x x0 )n
n
Solution:
(2x + 1)n+1
n2
(n + 1)
MATHEMATICS 3161: Fall 2013
Assignment # 4 (Due Date: Nov. 8)
5
2e3t
, y2 (t) =
are known to be solutions of the homogeneous
1
e3t
linear system y = Ay , where A is a real 2 2 constant matrix,
1. The
MATHEMATICS 3161: Fall 2013
Assignment # 5 (Due Date: Nov. 29)
1. Consider the initial value problem
y = ty,
y (0) = 1 ,
hand-calculate the rst ve iterations of Eulers method, the rst three iterations