Math 232, Test 3, 6 March 2007 Name: l-/iV1J1If~d Avu-wer:r
Instructions. Do each of the following six problems. Please do your best, and show all appropriate details in your solutions. Thank you!
. . dY 1. (10 pts) Fmd the general solutIOnto di
=[
.
.
-2
Math 232, Test 2, 12 February 2010
Name:
Instructions. Do each of the following questions. Please show all of your work. Good Luck!
dx
x
dy
(Short Answers) (a) Consider the system
= x 1
xy and
=
dt
2000
dt
y
2xy. Is this system more likely a model for a
Math 232, Final Test, 16 March 2010
Name:
Instructions. Do eleven of the following twelve problems. Please do your best, and show
all appropriate details in your solutions. Have a wonderful Spring break!
1. Solve the dierential equation
t
dy
=
subject to
Math 232, Test 3, 8 March 2010
Name:
Instructions. Do each of the following six problems. Please do your best, and show all
appropriate details in your solutions; you may not use a calculator.
1. (10 pts, short answers) (a) Given a 2 by 2 matrix A with tr
Math 232, Test 3, 2 March 2010
Name:
Instructions. Do each of the following six problems. Please do your best, and show all
appropriate details in your solutions; you may not use a calculator.
1. (a) (7 pts) Find the general solution to the system
dY
=
dt
Math 232, Test 2, 18 February 2011
Name:
Instructions. Do each of the following questions. Please show all of your work. Good Luck!
1. (Short Answers) For (i) and (ii), consider the rst-order system
x
dx
=x 1
+ xy
dt
2000
and
dy
y
= 3y 1
+ xy.
dt
3000
(i
Math 232, Test 2, 14 February 2008 Name: Instructions. Do each of the following questions. Please show all of your work. Good Luck! dY = AY is a system of dierential equations where A dt 1 1 has eigenvalues with corresponding eigenvectors: 2, and 3, . Wri
Math 232, Test 1, 1 February 2011
Name:
Instructions. Do each of the following eight questions. Please show all appropriate work in
your solutions in order to obtain maximum credit. You may use a calculator.
1. Solve the dierential equation
dy
1
= 4t3 y 2
Math 232, Test 1, 26 January 2010
Name:
Instructions. Do each of the following six questions. Please show all appropriate work in your
solutions in order to obtain maximum credit. You may use a calculator.
1. Solve the dierential equation
dy
3
= y + 2t3 e
Math 232, Test 1, 30 January 2007 Name: Instructions. Attempt each of the following seven questions. Please show all appropriate work in your solutions in order to obtain maximum credit. You may use a calculator. 1. Solve the differential equation dy = (y
Math 232, Final Test, 17 March
Name: W20 Mil/verif
Instructions. Do eleven of the following twelve problems. Please do your best, and show
all appropriate details in your solutions. Have a wonderful Spring break!
. . . dy t .
1. Solve the dlffer
Math 232, Final Test, 17 March
Name:
Instructions. Do eleven of the following twelve problems. Please do your best, and show
all appropriate details in your solutions. Have a wonderful Spring break!
1. Solve the dierential equation
t
dy
=
subject to y(0)
Math 232, Test 3, 6 March 2008 Name: Instructions. Do each of the following six problems. Please do your best, and show all appropriate details in your solutions. Thank you! 1. (10 pts) (a) Find the general solution to dY = dt 0 1 -1 -2 Y.
(b) Find the so
Math 232, Test 3, 6 March 2008 Name: Hints and Answers
Instructions. Do each of the following six problems. Please do your best, and show all appropriate details in your solutions. Thank you! 1. (10 pts) (a) Find the general solution to dY = dt 0 1 -1 -2
Math 232, Test 3, 6 March 2012
Name:
Instructions. Do each of the following six problems. Please do your best, and show all
appropriate details in your solutions. Thank you!
1. (a) (7 pts) Find the general solution to
dY
=
dt
6 4
1
2
Y.
(b) (3 pts) For th
Math 232, Test 2, 17 February 2012
Name:
Instructions. Do each of the following questions. You may not use a calculator. Please show
all of your work. Good Luck!
1. Find all equilibrium points for the system
2. Solve the partially decoupled system
dx
dy
=
Math 232, Test 1, 31 January 2012
Name: llmt '7: Amy/HUS.
Instructions. Do each of the following eight questions. Please ShOW all appropriate work in
your solutions in order to obtain maximum credit. You may use a calculator.
d 2
1. Find the general so
Math 232 Dierential Equations
Board Exercises, 10 January 2011
1. Solve
dP
= kP
dt
1
P
.
N
Answer. Separate variables:
N
dP =
P (N P )
left
1
1
+
P
N P
k dt. Use partial fractions on the integral on the
dP =
k dt
and then integrating to nd ln |P | ln |N P
Math 232, Practice Questions
Potential Practice: See your assignments, tests and tests from previous years. Notice this
year, there will be no question on Eulers method for systems, or hamiltonians and the nonlinear
pendulum which have been included on so
Math 232, Test 2, 18 February 2011
Name:
Instructions. Do each of the following questions. Please show all of your work. Good Luck!
1. (Short Answers) For (i) and (ii), consider the rst-order system
x
dx
=x 1
+ xy
dt
2000
and
dy
y
= 3y 1
+ xy.
dt
3000
(i
Math 232, Test 1, 31 January 2012
Name:
Instructions. Do each of the following eight questions. Please show all appropriate work in
your solutions in order to obtain maximum credit. You may use a calculator.
1. Find the general solution to the dierential