Math 3200-001 Quiz 7 - October 24, 2013
Question 1
Suppose you are given the vector ODE
y (t) = Ay (t)
(
where
A=
)
31
.
13
Question 1.a
Determine if y (t) solves that ODE
()
1
y (t) =
.
1
Answer 1.a
Plugging in to the ODE gives us
d
dt
() (
)( )
1
31
1
=
Math 3200-001 Exam 2 March 19, 2014
Closed book, closed notes, no calculators or other devices. One 3x5 handwritten card allowed, both sides.
1. Find a particular solution and general solution of the dierential equation
y + y 2y = 4et .
Solution. The char
Math 3200 Spring 2014
Exam 3
You may have only one 3x5 handwritten card, and the Laplace transform table handout.
1. Find the general solution of the dierential equation y (4) + 2y + y = 0.
2
Solution. The characteristic equation is 4 + 22 + 1 = 2 + 1 = 0
Math3200 Quiz 5 April 7 2014
Name:.
For multiple choice problems, please circle all correct answers. If none is
correct, write none". Each problem is worth 0 or 1 point.
1. The general solution of the dierential equation x(4)
t
t
(a) x = Ae + Be
t
x = 0 i
Math 3200 Spring 2014 Quiz 2 3/3/2014
Name:.
For multiple choice problems, Please circle all correct answers, or write none if none is
correct. Each problem is worth 0 or 1 point. For all other problems, solve the problem and
show your work.
1. The functi
Math 3195-001 Fall 2010 Quiz 7 11/3/10
Name:.
For multiple choice problems, please circle all correct answers. If none is correct, write
none. Each problem is worth 0 or 1 point.
1. The general solution of the dierential equation y + y = 1 is
(a) y = A si
Math 3200-001 Spring 2014 Quiz 7 4/23/1
Name:.
For multiple choice problems, please circle all correct answers. If none is correct, write none.
No books, notes, or calculators allowed. Each problem is worth 0 or 1 point.
1. The eigenvalues and eigenvector
Math3200 Quiz 6 April 14 2014
Name:.
For multiple choice problems, please circle all correct answers. If none is
correct, write none. Each problem is worth 0 or 1 point.
1. The dierential equation x + 3x + 7x = t2 is equivalent to the ODE
system
x1 = x2
x
Quiz 4 March 17 2014 solution
1. The equation y + y = sin x
(a) describes a resonance (b) has a bounded solution
(c) has solutions with beats (d) describes forced oscillation with damping
Solution. The homogeneous equation has general solution A sin (x ),
Math 3200-001 Spring 2014
Final exam
You may have one 3x5 index card and the page with Laplace transform (you
can have notes on it also, both sides).
When you start the solution, always copy the statement of the problem rst.
1. Find the general solution o
Math 3200-002 Quiz 1 - August 28, 2012
Question 1
For each of these problems, assume t > 0. Determine all values of k which makes yk a solution to
the given ODE. If there are none, say so.
Question 1.a
y + y 2 = 0,
yk (t) =
k
.
t
Answer 1.a
Plug in the su
Math 3200-001 Quiz 8 - November 5, 2013
Question 1
(
Solve the IVP
y=
)
13
y,
31
()
1
y (0) =
.
1
It may help to know that
(
13
31
)(
)(
)(
)
1 1
1 1
2 0
=
11
11
04
but youll only know why if you paid attention during class.
Answer 1
(
)
We make our stand
Math 3200-001 Quiz 9 - November 14, 2013
Question 1
Compute the Laplace transform of
f (t) = te2t .
Answer 1
Recall that
1
s2
at
Lcfw_e g (t) = G(s a)
Lcfw_t =
We can identify g (t) = t, which means that
F (s) = Lcfw_f (t) =
1
1
.
(s + 2)2
Question 2
Solv
Math 3200-001 Quiz 10 - November 21, 2013
Question 1
Suppose you have a black box system which is initially at rest. When you apply an input f (t) =
2h(t 1) you observe the output y (t) = (t 1)2 h(t 1).
Question 1.a
Determine the system transfer function
Math 3200-001 Quiz 6 - October 10, 2013
Question 1
Consider the second order linear dierential operator
L=
d2
d
+ p(t) + q (t),
2
dt
dt
so that Ly = y + p(t)y + q (t)y . Lu1 = t2 and Lu2 = e2t .
Question 1.a
What linear combination of u1 and u2 solves the
Math 3200-001 Quiz 5 - October 1, 2013
Question 1
For the ODE
y + by + cy = 0,
you know one solution is y1 (t) = et and you use reduction of order to nd y2 (t) = tet . Find b and
c such that these are the component solutions.
Answer 1
As is often the case
Math 3200-001 Quiz 2 - September 10, 2013
Question 1
Solve the linear rst-order IVP
y 2y = e2t ,
y (0) = 1.
Answer 1
You guys got o easy - apparently the question I gave to the other class was way hard. For this
one you just need an integrating factor: (t
Math 3200-001 Quiz 3 - September 17, 2013
Question 1
This question deals with the IVP
2yy + 3t2 = 0,
y (1) = 1.
Question 1.a
Find an implicit solution and, if possible, and explicit solution.
Answer 1.a
This is a separable problem which happens to already
Math 3200-001 Quiz 4 - September 24, 2013
Question 1
Try and solve the second order IVP
y y = 0,
y (0) = 1, y (0) = 2,
using the component solutions
y1 (t) = et ,
y2 (t) = et+1
to form the general solution
y (t) = Aet + B et+1 .
Explain what is happening.
Math 3200-001 Spring 2014 Quiz 8 4/28/1
Name:.
For multiple choice problems, please circle all correct answers. If none is correct, write
none. No books, notes, or calculators allowed. You may have the Laplace transform table.
Each problem is worth 0 or 1