Math 324 Homework 2 Solutions
Instructor: J. Metcalfe
Section 7.1, # 39. The unit staircase function is dened as follows:
f (t) = n if n 1 t < n, n = 1, 2, 3 . . .
a. Sketch the graph of f to see why
Math 302 - Dierential Equations (Metcalfe)
Summer 2001 June 18, 2001
Method of Undetermined Coecients (Section 3.6, 4.3) When: Use this technique to solve linear nonhomogeneous equations when the forc
Math 302 - Dierential Equations (Metcalfe)
Summer 2001 June 3, 2001
Solving Linear, Homogeneous Second-Order Equations with Constant Coecients (Sections 3.1,3.4 When: Use this technique for linear hom
Math 302 - Dierential Equations (Metcalfe)
Summer 2001 May 31, 2001
Solving Separable Equations (Section 2.2) When: Use this technique for rst-order separable equations. A separable equations is one t
Math 324 Homework 10 Solutions
Instructor: J. Metcalfe Section 8.3 # 20 Find two linearly independent Frobenius series solutions (for x > 0) of 3xy + 2y + 2y = 0. We first notice that x0 = 0 is a regu
Math 324 Homework 6 Solutions
Instructor: J. Metcalfe
3 Section 7.4, # 26 Find the inverse transform of F (s) = tan1 s+2 .
We apply Theorem 2: 1 f (t) = L1 cfw_F (s) t 1 3 1 = L1 3 2 (s + 2)2 t 1 + (
Math 524 - Elementary Dierential Equations
Instructor: J. Metcalfe Due: March 27, 2008
Assignment 17 Section 5.4, # 8 Find the general solution to 25 12 0 x = 18 5 0 x. 6 6 13 Since 0 = det A I = ( 13
Math 324 Homework 6 Solutions
Instructor: J. Metcalfe Section 8.1, # 14 Use the method of Example 4 to nd two linearly independent power series solutions of the dierential equation y + y = x. Determin
Chapter 2
Linear Algebra
Introduction
The purpose of this chapter is to provide sufficient background in linear
algebra for understanding the material of Chapter 3, on linear systems of
differential e
Single Differential
Equations
Michael Taylor
Contents
1. The exponential and trigonometric functions
2. First order linear equations
3. Separable equations
4. Second order equations reducible cases
5.
Chapter 3
Linear Systems of
Differential Equations
Introduction
This chapter connects the linear algebra developed in Chapter 2 with Differential Equations. We define the matrix exponential in 1 and s
Math 302 - Dierential Equations (Metcalfe)
Summer 2001 June 5, 2001
Reduction of Order When: We know that the general solution of a second-order, linear homogeneous dierential equation consists of two
Math 302 - Dierential Equations (Metcalfe)
Summer 2001 June 26, 2001
Series Solutions Near an Ordinary Point (Section 5.2) When: This technique can be used to solve linear homogeneous dierential equat
Math 324 Homework 3 Solutions
Instructor: J. Metcalfe
Section 7.2, # 34 If f (t) = (1)[t] is the square-wave function (whose graph is given on p. 463
of your book), then
1
s
Lcfw_f (t) = tanh
s
2
.
De
Math 324 Homework 6 Solutions
Instructor: J. Metcalfe
3
Section 7.4, # 26 Find the inverse transform of F (s) = tan1 s+2 .
We apply Theorem 2:
1
f (t) = L1 cfw_F (s)
t
1
3
1
= L1
3 2 (s + 2)2
t
1 + (
Math 324 Homework 6 Solutions
Instructor: J. Metcalfe
Section 8.1, # 14 Use the method of Example 4 to nd two linearly independent power series
solutions of the dierential equation y + y = x. Determin
Math 324 Homework 12 Solutions
Instructor: J. Metcalfe
8.4 # 10 Find the rst four nonzero terms in a Frobenius series solution of x2 y +xy +(x2 +1)y = 0.
Then use the reduction of order technique (as
Math 524 - Elementary Dierential Equations (Metcalfe)
Fall 2008
September 25, 2008
Exam 1
Please show all of your work, and justify your answers completely. No credit will be given for
answers which a
Math 524 - Elementary Dierential Equations (Metcalfe)
Fall 2008
November 6, 2008
Exam 2
Please show all of your work, and justify your answers completely. No credit will be given for
answers which are
Math 302 - Dierential Equations (Metcalfe)
Summer 2002
June 4, 2002
Exam 1 - Practice Exercises
1. Find a general solution to
dy
2
+ xy = ex /2
dx
2. Find a solution of:
(3x4 y 1) dx + x5 dy = 0;
y (1
Math 302 - Dierential Equations (Metcalfe)
Summer 2002
June 17, 2002
Exam 2 - Practice Exercises
1. Find a solution to the initial value problem
y 2xy + 8y = 0;
y (0) = 3,
y (0) = 0
2. Find a general
Math 302 - Dierential Equations (Metcalfe)
Summer 2002
June 23, 2001
Final Exam - Practice Exercises
1. Write
3y (4) 5y + 9y = 6et 2t
as a system of linear, rst order dierential equations.
2. Find the
Math 324 Homework 3 Solutions
Instructor: J. Metcalfe Section 7.2, # 34 If f (t) = (1)[t] is the square-wave function (whose graph is given on p. 463 of your book), then 1 s Lcfw_f (t) = tanh s 2 . De
Chapter 4
Nonlinear Systems of
Dierential Equations
Introduction
This final chapter brings to bear all the material presented before and pushes
on to the heart of the subject, nonlinear systems of die