MATH 341, Exam II, Version 1, Fall 2014
1. (25) You have the system of dierential equations x = Ax where A =
for which x(0) =
0 1
. Find the solution
1 0
1
.
2
1 1 0
. Row
1 1 0
1 1 0
1
1 1 0
1 1 0
ops give
and u multiple of
. For r = 1, get
. Row ops giv
MATH 341: Exam I, Fall 2013
Key
There are two slightly dierent versions of this exam. This Key is for one of them.
dy
1. (10) Find all the solutions of
= 3xy 3 .
dx
First order nonlinear. Separate variables.
y 3 dy =
1 2
y
=
2
3xdx
3 2
x +C
2
implicit sol
MA 341 Test 1 Version 1 Spring 2016 No Work:No Credit!
4
. d
l.(18pomts) Use —y= y
dx 6-3xy3
to answer the following
a) Show that for y>0, the equation 6ln(y)—xy3 = C is an implicit solution
b) Find the value of C for which this equation gives a solutio
MA 341 Test 3 Version 1 Show ALL of your work.
0 l 3
1. (10 points) Use the method of undetermined coefficients to find a particular solution to i’ zi 5 1J1”: +L OJ
Iiint: [Jon'tiind x“!
1 —2 3
2. (8 points) The matrix —2 1 —3 has the characteristic polyn
I!
l
l
!
MA 34] Test 1 Version 2 Spring 2016 No Work:No Credit!
3
1. (18 points) Use d—y= 5’ ,
dx 4-2xy"
a) Show that for y>0, the equation 41n(y)—xy2 = C is an implicit solution
b) Find the value of C for which this equation gives a solution to the initi
Math 2171 (Differential Equations)
Final Exam - Extra Credit DUE IN CLASS 12/16/2009
1. (Convolutions) (10 points)
(a) (1 point) Use the convolution theorem to nd the Lapalce transform F (s) of
t
e(t ) sin d.
f (t) =
0
(b) (1 point) Use the convolution th
Math 2171 (Differential Equations)
Exam 2 - Extra Credit DUE 12/02/2009
1. (2 points) Consider the following initial value problem.
x
y
=
cos t et sin t
1
ln t
1+t2
x
cot t
+
y
cosh 1
t
,
x(t0 )
y(t0 )
=
x0
y0
Is it true that for any x0 and y0 the above s
Math 2171 (Differential Equations)
Exam 1 - Extra Credit DUE 10/21/2009
MULTIPLE CHOICE Read all the answer choices before responding.
1. (1 point) The rst order dierential equation
dy
dt
= f (t, y) is autonomous if
(a) f (t, y) is any function.
(b) f (t,
MATH 2171 Section 004 - Fall 2009
Study Guide for Exam #1
Coverage: Sections 1.1-1.4, 2.1-2.6
Know how to classify differential equations by:
order
ordinary vs. partial
linear vs. nonlinear
Know how to plot a direction eld by hand (especially for aut
MATH 2171 Section 004 - Fall 2009
Study Guide for Exam #2
Coverage: Sections 3.1-3.4, 4.1-4.6.
Section 3.1-3.2:
For a 2x2 matrix A:
Know how to calculate its determinant.
Know how to calculate its matrix inverse, and how to use this inverse to solve Ax
MATH 2171 Section 004 - Fall 2009 - Study Guide for Final Exam
Book Coverage: Sections 1.1-1.4, 2.1-2.6, 3.1-3.4, 4.1-4.6, 5.1-5.8.
Chapter 1
Drawing and interpreting direction elds (section 1.1).
Applying Eulers method to a rst order IVP: y(t)=f(t,y) w