Ma 530 Method of Frobenius - Some Examples
Example 1
Use the method of series solution near a regular singular point to find a Frobenius solution to
x 2 y xy x 2 4 y 0
and show that it can be written as
1 n x 2n2
2n1 n 2!n!
n0 2
y1
Solution:
x2 4
y 1x y

MAT3320 Assignment 1
Total: 10 marks. Due date: Tuesday, Sept 29, before 6:00pm. In MATH Department (585
King Edward), there is a Drop-Box. You need to put your assignment into the box before
6:00pm on the due date. Late assignments will not be accepted.

MAT3320 Assignment 2
Total: 10 marks. Due date: Tuesday, Oct 13, before 6:00pm. In MATH Department (585
King Edward), there is a Drop-Box. You need to put your assignment into the box before
6:00pm on the due date. Late assignments will not be accepted.
1

MAT3320 Assignment 4
Total: 10 marks. Due date: Tuesday, Dec 1, on or before 6:00pm. In MATH Department (585 King Edward), there is a Drop-Box. You need to put your assignment into the box
before 6:00pm on the due date. Late assignments will not be accept

MAT3320 Assignment 3
Total: 10 marks. Due date: Tuesday, Nov 10, on or before 6:00pm. In MATH Department
(585 King Edward), there is a Drop-Box. You need to put your assignment into the box before
6:00pm on the due date. Late assignments will not be accep

MAT3320 Assignment 4
Total: 10 marks. Due date: Tuesday, Dec 1, on or before 6:00pm. In MATH Department (585 King Edward), there is a Drop-Box. You need to put your assignment into the box
before 6:00pm on the due date. Late assignments will not be accept

1
Introductory lecture notes on Partial Dierential Equations - c Anthony Peirce.
Not to be copied, used, or revised without explicit written permission from the copyright owner.
Lecture 5: Examples of Frobenius Series: Bessels Equation
and Bessel Function

MAT3320 Assignment 2
Total: 10 marks. Due date: Oct. 7th;
1. (3 marks) Let f (x) = x3 , 2 < x < 6. Find the Fourier-Legendre expansion.
2. (6 marks=1+1+2+2) Consider the following equation:
2xy + y + 3y = 0.
(a) Show that x0 = 0 is a regular singular poin

MAT3320 Assignment 1
Total: 10 marks. Due date: Sept. 26th;
1. (6 marks) Consider the following DE y + xy + 2y = 0.
(a) (3 marks) Find the coecient recursion relation for the general series solution about
x0 = 0.
(b) (2 marks) Find two linearly independen

MAT3320 Brief Review
Homogeneous second order linear eqn: ay + by + cy = 0. Let r1 and
r2 be two solutions of the indicial eqn ar2 + br + c = 0.
r1 = r2 : y = c1 er1 x + c2 er2 x .
r1 = r2 : y = (c1 + c2 x)erx .
r = + i: y = ex (c1 cos x + c2 sin x).

MAT3320 Assignment 3
Total: 10 marks. Due date: Tuesday, Nov 10, on or before 6:00pm. In MATH Department
(585 King Edward), there is a Drop-Box. You need to put your assignment into the box before
6:00pm on the due date. Late assignments will not be accep

MAT3320 Assignment 2
Total: 10 marks. Due date: Tuesday, Oct 13, before 6:00pm. In MATH Department (585
King Edward), there is a Drop-Box. You need to put your assignment into the box before
6:00pm on the due date. Late assignments will not be accepted.
1

MAT3320 Assignment 1
Total: 10 marks. Due date: Tuesday, Sept 29, before 6:00pm. In MATH Department (585
King Edward), there is a Drop-Box. You need to put your assignment into the box before
6:00pm on the due date. Late assignments will not be accepted.