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 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

Fall 2015
Midterm #2
(Please do not use Laplace Transform)
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Last Name: Q (A U " Ll" l FirstName:
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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
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MIDTERM #1
First Name:
,Xdy + ydx = 3x2dx/_)
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2. Solve the following equation.
The initial condition is y(1)=1
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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
Introduction to Differential Equations and Applications
AMATH 351

Winter 2014
AMATH 351 Winter 2015
Extra Credits
Due: 10:30am Friday March 13th , 2015
This assignment is worth up to 5% on your nal grade. Each problem worths 1%.These problems
are not meant to be easy and there is no need to nish every problem.
Read FAQ No.11 rst.
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
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
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
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
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
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
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
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 < .
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 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 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 =
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
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
April 30, 2012
Lecture 15
Second order linear ODEs
 nonhomogenous equations
Lecturer: Jiri Najemnik
Rererecall what the linear SECOND ORDER ODEs are
General linear second order equation (in a convenient form for us)
p t y t q t y t r t y t s
AMATH 351
April 23, 2012
Lecture 13
Second order linear ODEs pt. 3
instructor: Jiri Najemnik
Recall what the linear SECOND ORDER ODEs are
General linear second order equation (in a convenient form for us)
p t y t q t y t r t y t s t
Homogenous linear sec