Possibly helpful formulas and models
1
du = ln |u| + C
u
du
= arctan u + C
1 + u2
eu du = eu + C
un1 sin u du
un cos u du = un sin u n
nu
nu
u e du = u e n
n 1 u
u
un eu du = n!
e du
0
Equation of mot
Page 1
1. (5) The following picture is a slope eld for the differential equation % = a: + y. Suppose y(:z:)
is a solution to the initial value problem 73 = :1: + y, y(0) = 2. Without nding y explicitl
Math 3113 homework
1. (assigned 1/19) Study the course syllabus. Make sure you know the meaning of the
following terms: equation, dierential equation, ordinary dierential equation, partial
dierential
Math 3113 homework
29. (assigned 3/9) Prepare for Quiz 5 on Friday. Over the spring break, do 3.5 # 47. Try
to do it (i) rst by the single formula in Theorem 1 of Section 3.5, then (ii) from the
two e
Math 3113 homework
38. (assigned 4/11) 5.2 # 2, 3, 4 (do not do the part of the problem that asks you to use
a computer system or graphing calculator, just use the eigenvalue method to nd the
general
Math 3113 homework
13. (assigned 2/11) Study the posted Quiz 2 solutions. The class performance on Quiz 2
was generally not what it should be, partly due to not following the instructions of the
probl
Math 3113 homework
22. (assigned 2/25) Check the posted solutions of Quiz 3 to see what you didnt know
about the theory. This will help you determine what gaps you have in your knowledge
of sections 3
Mathematics 3113-005
Name (please print)
Quiz 1 Form A
January 28, 2011
Instructions: Give concise answers, but clearly indicate your reasoning. Most of the problems have rather short
answers, so if y
Mathematics 3113-005
Name (please print)
Quiz 1 Form A
January 28, 2011
Instructions: Give concise answers, but clearly indicate your reasoning. Most of the problems have rather short
answers, so if y
Mathematics 3113-005
Name (please print)
Quiz 1 Form B
January 28, 2011
Instructions: Give concise answers, but clearly indicate your reasoning. Most of the problems have rather short
answers, so if y
Mathematics 3113-005
Name (please print)
Quiz 1 Form B
January 28, 2011
Instructions: Give concise answers, but clearly indicate your reasoning. Most of the problems have rather short
answers, so if y
Mathematics 3113-005
Name (please print)
Quiz 2 Form B
February 11, 2011
Instructions: Give concise answers, but clearly indicate your reasoning.
I.
(3)
For the rst-order linear homogeneous DE y + P (
Mathematics 3113-005
Name (please print)
Quiz 2 Form A
February 11, 2011
Instructions: Give concise answers, but clearly indicate your reasoning.
I.
(3)
dy
Check whether the initial value problem
= y
Mathematics 3113-005
Name (please print)
Quiz 2 Form A
February 11, 2011
Instructions: Give concise answers, but clearly indicate your reasoning.
I.
(3)
dy
Check whether the initial value problem
= y
Mathematics 3113-005
Name (please print)
Quiz 2 Form B
February 11, 2011
Instructions: Give concise answers, but clearly indicate your reasoning.
I.
(3)
For the rst-order linear homogeneous DE y + P (
Mathematics 3113-005
Name (please print)
Quiz 3 Form A
February 25, 2011
Instructions: Give concise answers, but clearly indicate your reasoning.
I.
Two linearly independent solutions of the DE y + 3y
D
IFFERENTIAL
E
QUATIONS
Erin P. J. Pearse
These notes follow Dierential Equations and Boundary Value Problems (4ed) by C. H.
Edwards and D. E. Penney, but also include material borrowed freely from o
Linear Independence & Dierential Equations
Denition 1. A set of functions cfw_y1 , . . . , yn , yi : I R, is linearly independent i
you cannot write one function as a linear combination of the others.
Partial Fractions Review
Introduction. The goal of partial fraction decomposition is to rewrite a rational function in a simpler form: split it into a sum of smaller rational functions where each de
Practice Exam 1a
1. Solve the IVP:
2. Solve the ODE:
3. Solve the ODE:
dy
= y , y (0) = 2.
dx
dy
1+ x
=
.
dx
1+ y
(1 + ex )
2(ey + x3 e2x )dx xey dy = 0.
4. 100L of a brine solution is diluted with pu
MATH 3113, HOMEWORK 1, SOLUTIONS, DUE THURSDAY
JANUARY 23
1. Sketch the set of points z C determined by the condition
|z 1 + i| = 1.
This is the circle with radius 1 centered at 1 i.
2. Prove that for
MATH 3113, HOMEWORK 4, SOLUTIONS, DUE THURSDAY
FEBRUARY 13
0. Sections you should be familiar for the test:
Laplace transform tables and the tables of integrals at the beginning and at the end of
the
MATH 3113, HOMEWORK 3, SOLUTIONS, DUE THURSDAY
FEBRUARY 6
1. There is an RLC electric circuit in a black box and your job is to nd out R, L and C.
However, your friend from ASN told you that whoever c