Introduction to Differential Equations and Applications
AMATH 351

Fall 2015
AMATH 351 Summer 2015
Homework 2
Due: Wednesday, October 21, 2015
Show work for full credit! The grader will subtract points for poor presentation.
1. (Breaking Bad II) Hank Schrader is the man in charge of the Drug Enforcement
Administration (DEA) in Alb
Introduction to Differential Equations and Applications
AMATH 351

Winter 2014
Introduction to dierential equations and applications
Bernard Deconinck
Department of Applied Mathematics
University of Washington
Campus Box 352420
Seattle, WA, 98195, USA
October 2, 2009
Prolegomenon
These are the lecture notes for Amath 351: Introducti
Introduction to Differential Equations and Applications
AMATH 351

Winter 2014
Dierential Equations Midterm
Name:
Student Number:
November 16, 2011
(15 pts) 1. Consider the equation
dy
= y y3
dt
Find all of the critical points, sketch several solutions for the equation
in typlane, and determine whether each critical point is asympt
Introduction to Differential Equations and Applications
AMATH 351

Fall 2015
AMATH 351 Autumn 2015
Homework 1
Due: Wednesday, October 14, 2015
Show work for full credit! The grader will subtract points for poor presentation.
1. (Falling Object) A model for the velocity v of an object falling is given by
dv
= mg v,
dt
where m is th
AMath 351
Spring 2014
Prof. Ido Bright
Alex Goodfriend
Homework 4: Sample solutions
1. Find the general solution of the given dierential equation.
These are all linear, homogeneous, secondorder ODEs with constant coecients, so we apply the usual
method ba
AMath 351
Spring 2014
Prof. Ido Bright
Alex Goodfriend
Homework 5: Sample solutions
1. Solve the following equations using the method of undetermined coecients:
(a) y + y 2y = sin x, y(0) = 1, y (0) = 2:
The associated homogeneous equation is secondorder
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What else might we want to know about a population?
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What commonly goes into composition?
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What are some of the ways demographers pay attention to change over time?
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AMATH351, SPRING 2014 HOMEWORK 6
SHOW ALL YOUR WORK FOR FULL CREDIT!
Submit on: Friday May 23rd, 10:30AM in class.
(1) Write the given system dierential equation as a system of rst order dierential
equations.
u + 3v = 4u3
(a)
v + u 2 = v + u
u v = 3 3 u
(
AMath 351
Spring 2014
Prof. Ido Bright
Alex Goodfriend
Homework 6: Sample solutions
1. Write the given system of dierential equations as a system of rstorder dierential equations.
(a)
u + 3v
v + u2
= 4u3
The idea here is to dene a new set of variables so
AMath 351
Spring 2014
Prof. Ido Bright
Alex Goodfriend (TA)
Homework 3: Sample solutions
1. Solve the dierential equations:
(a) Find all solutions of
y + 2y = y 2 ex
by substituting u = 1/y.
We will need the following relations: y = 1/u, y 2 = 1/u2 , y =
AMATH351, SPRING 2014 HOMEWORK 3
SHOW ALL YOUR WORK FOR FULL CREDIT!
Due: Friday Apr 25th, 10:30AM in class.
(1) Solve the dierential equations:
(a) Find all solutions of
y + 2y = y 2 ex
by substituting u = 1/y.
(i) Find the solution for the initial condi
AMath 351
Spring 2014
Prof. Ido Bright
Alex Goodfriend (TA)
Homework 2: Sample solutions
1. Solve the dierential equations. (Use all methods studied in the rst 2 weeks of the course.)
(a) xy =
1 y2
Case 1: 1 y 2 = 0
dy
= dx
2
x
1y
dy
1y 2
=
dx
x
arcsin(y
AMATH351, SPRING 2014 HOMEWORK 2
SHOW ALL YOUR WORK FOR FULL CREDIT!
Due: Friday Apr 24th, 10:30AM in class.
(1) Solve the dierential equations. (Use all methods studied in the rst 2 weeks of
the course.).
(a) xy =
1 y2
(b) y + y tan x = sin 2x,
< x < .
AMATH351, SPRING 2014 HOMEWORK 1
SHOW ALL YOUR WORK FOR FULL CREDIT!
Due: Friday Apr 11th, 10:30AM in class.
(1) For each of the following equations, specify its order and whether it is linear or
nonlinear.
(a) y = y.
(b) x2 y = y + 3
(c) xy cos (y) x x6
AMath 351
Spring 2014
Prof. Ido Bright
Alex Goodfriend (TA)
Homework 1: Sample solutions
1. For each of the following equations, specify its order and whether it is linear or not:
(a) y = y: rstorder, linear
(b) x2 y = y + 3: thirdorder, linear (althoug
Introduction to Differential Equations and Applications
AMATH 351

Fall 2015
Midterm #2
(Please do not use Laplace Transform)
ID: n ' ' Jim/A
Last Name: Q (A U " Ll" l FirstName:
#1 Solve 3y+2x/§y'+y=0, y(0)=2\/§, y(0)=3
art} $¢T1>
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Introduction to Differential Equations and Applications
AMATH 351

Fall 2015
AMATH 351
Last Name: SO A; 
Student ID :
1. Solve the following equation
6%
0%. TM $91,041,
MIDTERM #1
First Name:
,Xdy + ydx = 3x2dx/_)
d W l
% (Zen)
2. Solve the following equation.
The initial condition is y(1)=1
3' 3613) a ($10
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Introduction to Differential Equations and Applications
AMATH 351

Fall 2015
AMATH 352  Hw1 ex2 Result  Attempt 1
Student: tianzw
Homework: Hw1
Exercise: ex2
Attempt: 1
Time: 2014116 23:46:1
File VecX.dat > Value is within the range !
File VecY.dat > Value is within the range !
Score for this attempt: 8 / 8
clear al
Introduction to Differential Equations and Applications
AMATH 351

Winter 2014
George Ueda Final Review
Quiz Sections AD & AG
Bioc441 Winter 2015
Photosynthesis
1. When electrons in the antenna complex of photosystem II are excited by
photons, energy is transferred down to the core reaction center by a process
called resonance energ
Introduction to Differential Equations and Applications
AMATH 351

Winter 2014
Assignment 3
Due Friday, 7/11/2014
Remember to show your work for credit!
Problem 1
Solve each of the following linear, second order equations. If initial conditions are
given, solve for any constants.
(a) 4y y = 0, y(2) = 1, y (2) = 1.
(b) y + 5y + 6y =
Introduction to Differential Equations and Applications
AMATH 351

Winter 2014
Dierential Equations Final
Name:
Student Number:
January 11, 2012
(12 pts) 1. Find the solution of the given initial value problem
y + 4y = 2t2 + 5et ,
y (0) = 2
y(0) = 1,
Sol. The characteristic equation for the homogeneous problem is
r2 + 4 = 0, with co
GEOG 245: Geodemographics
Autumn 2016
Using American FactFinder
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online. The website is run by the Census Bureau and includes all of the publicly available data
that th
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Introduction to Differential Equations and Applications
AMATH 351

Spring 2014
Some important calculus stuff
Pedro D. Maia
This homework wont be graded for several reasons: its long, its hard and its about
material youve covered in previous courses. When I was learning calculus for the first
time, I was not able to fully appreciate
Introduction to Differential Equations and Applications
AMATH 351

Spring 2014
AMATH 351 Summer 2015
Homework 3
Due: Wednesday, October 28, 2015
Prepare for Exam Part A
The grader wont be able to return this homework
graded to you before the exam. I recommend that
you make a copy of your solutions so you may
compare it with mine bef
Introduction to Differential Equations and Applications
AMATH 351

Spring 2014
AMATH 351
Homework 1
Due at time and place posted on website
Show work for full credit! The grader will subtract points for poor presentation.
1. (Falling Object) A model for the velocity v of an object falling is given by
dv
= mg v,
dt
where m is the mas