2)
Using Matlab2008a %:
% phi_0(t) = 2/(1  2t) and phi_1(t) = (3 + e^cfw_2t)/(3  e^cfw_2t)
%
% Part B
f=@(t,y) y.^2exp(t.^2)
figure, hold on
ode45(f,[0 .5*log(3)],2)
ode45(f, [0 0.54],2)
% Problem 4
% Part A
f=@(t,y) (y(t^1/2)*(1y^2);
figure, hold o
MATH 246  Quiz 4 Solutions
Monday, June 16th, 2014
(1) Suppose that ex sin x and ex cos x satisfy
d2 y
dy
+ 2y = 0.
2
dx2
dx
Find the natural fundamental solutions N0 (x) and N1 (x) associated with this dierential equation.
Solution: A general solutions
Third InClass Exam Solutions
Math 246, Professor David Levermore
Thursday, 29 November 2012
(1) [6] Given that 2 is an eigenvalue of the
2
1
A=
3
matrix
2 1
1
0,
1 1
nd all the eigenvectors of A associated with 2.
Solution. The eigenvectors of A associat
Patrick Fernandes & Brayton Bushby
Math246, 0222
10 April 2009
Matlab: Problem Set D
3. A
close all;
rhs= @(t,y) [y (2); sin (y (1)];
figure, hold on
rhs= @(t,y) [y (2); sin (y (1)];
[xa,ya]=ode45 (rhs, [0 10], [.1 0]);
val= [xa, ya (:,1)];
plot (xa,ya
Chapter 11
Solving and Analyzing Second
Order Linear Equations
Newtons second law of dynamicsforce is equal to mass times accelerationtells physicists that, in order to understand how the world works, they must pay attention to forces.
Since acceleration
Chapter 15
Qualitative Theory for
Systems of Differential
Equations
In this chapter, we extend the qualitative theory of autonomous differential equations from
single equations to systems of two equations. Thus we consider a system of the form
x = F (x, y
Chapter 10
Using Simulink
Simulink is a useful auxiliary to MATLAB, which is automatically included in the MATLAB Student Version; with the Professional Version, it can be obtained as an additional
toolbox. In this chapter, we give a concise introduction
Credits: 3 : Prerequisite: MATH141; and (PHYS171, PHYS161, ENES102, or MATH240). Credit only grante
MATH 246

Fall 2013
Mathematics 246/246H, Fall Semester, 2004
Final Examination
Monday, December 13, 2004
Instructions. Answer each question on a separate answer sheet, with a
number that corresponds to the number of the problem. Please make sure
that your name, section numb
Exam 1 July 30, 2006 Joel M. Cohen Name: Math 246 9:30  10:50 a.m.
Calculators are not allowed. Read the problems very carefully! CIRCLE your final answer to each problem! When possible, express solutions explicitly. Show all your work on these pages, us
Final Exam Sample Problems, Math 246, Fall 2013
dy
= (9 y 2)y 2 .
dt
(a) Identify its stationary points and classify their stability.
(b) Sketch its phaseline portrait in the interval 5 y 5.
(c) If y (0) = 1, how does the solution y (t) behave as t ?
(1)
Chapter 2
Getting Started with MATLAB
In this chapter, we will introduce you to the tools you need in order to begin using MATLAB effectively. These include: some relevant information on computer platforms and
software versions; installation protocols; ho
Preface
Computers have at least three important uses in a differential equations course.
The rst is simply to crunch numbers, thereby generating accurate numerical
approximations to solutions. The second is to carry out symbolic manipulations that would b
Chapter 1
Introduction
We begin by describing the philosophy behind our approach to the study of ordinary differential equations. This philosophy has its roots in the way we understand and apply differential equations; it has inuenced our teaching and gui
Math 246  Exam 3 Solutions
Thursday, July 3rd, 2014
(1) Recast the following higherorder dierential equations into rst order systems. If the
equation is linear, be sure to give the coecient matrix A(t) and the forcing f (t).
2
(a) (1 + t2 )y + et y sin
Math 246  Exam 2 Solutions
Monday, June 23rd, 2014
(1) In the following problem D =
d
.
dt
(a) Give a general solution to the following dierential equation
D3 (D2 + 9)2 (D2 2D 7)2 (D2 + 2D + 10)y = 0.
(b) What is the order of the dierential equation in (
Math 246  Exam 1 Solutions
Wednesday, June 11th, 2014
(1) [16 pts] Solve the following initial value problems and give their intervals of denition.
(a)
1 z2
dz
= 2
,
dx
x 1
z(0) = 0.
(b)
dy
z 4 ez + 2zy
=
,
dz
z2
y(1) = 0.
Solution:
(a) This equation is
MATH 246 Quiz 1 Solutions
Wednesday, June 4th, 2014
(1) [2ts] For the dierential equation below, state the order and whether it is linear or
nonlinear.
dg 2x 3
d2 g
+ g = 0.
g 2 (1 x2 )g
dx
dx
g
Solution: Divide the equation by g. The equation is second o
MATH 246  Quiz 3 Solutions
Tuesday, June 10th, 2014
(1) Suppose that you are using the explicit (forward) Euler method to solve a dierential
equation. If you decrease the step size h by a factor of 10, by what factors will the
local and global errors dec
MATH 246 Quiz 2 Solutions
Friday, June 6th, 2014
(1) [5pts] Find the solution to the initial value problem
dx
= te2x ,
dt
x(0) = xI , for xI in (, ).
Give its interval of denition in terms of xI .
Solution: Putting this in factored dierential form and int
MATH 246, SPRING 2014 SECTIONS 01XX, MWF
11:00AM  11:50AM ARM 0126
A current, updated copy of this syllabus will be available
http:/www2.math.umd.edu/ matei/
Dr. M. Machedon, Math Bldg. 3311. email: mxm@math.umd.edu
Oce hours: Mondays and Wednesdays fro
Solutions to Third InClass Exam
Math 246, Professor David Levermore
Tuesday, 26 November 2013
(1) [6] Given that 2 is an eigenvalue of the matrix
2 1 3
A = 1 2 2 ,
2 1 3
find all the eigenvectors of A associated with 2.
Solution. The eigenvectors of A as
First InClass Exam Solutions
Math 246, Professor David Levermore
Thursday, 27 September 2012
dz
(z 2 9)(9 z)
=
.
dt
9 + z2
[6] Sketch its phaseline portrait over the interval 6 z 12. Identify all
of its stationary (equilibrium) solutions and classify ea
Second InClass Exam Solutions
Math 246, Professor David Levermore
Thursday, 25 October 2012
(1) [4] Give the interval of definition for the solution of the initialvalue problem
7
3
z + 2
z =
,
z(4) = z (4) = z (4) = 0 .
t 25
sin(t)
Solution. The equatio
Solutions of Sample Problems for Second InClass Exam
Math 246, Fall 2015, Professor David Levermore
(1) Give the interval of definition for the solution of the initialvalue problem
e2t
d3 x cos(3t) dx
=
,
+
dt3
4 t dt
1+t
x(2) = x0 (2) = x00 (2) = 0 .
S
Solutions to Second InClass Exam
Math 246, Professor David Levermore
Tuesday, 29 October 2013
(1) [4] Give the interval of definition for the solution of the initialvalue problem
u
3 cos(5t)
et
u +
u=
,
t
6+t
2t
u(3) = u (3) = u (3) = 0 .
Solution. The