Spring 2013 Math 308-503
Exam 1A: Solutions
c Art Belmonte
Sun, 10/Feb
3. Solve the differential equation
(ax + by) dx + (bx + cy) dy = 0
by hand. Show your steps. Check via deSolve if
desired.
1. Solve the differential equation
ty + 2y = sint
by hand. Sh
Spring 2013 Math 308-503
Exam 1B: Solutions
c Art Belmonte
Sun, 10/Feb
3. Solve the differential equation
xy2 + 3x2 y dx + x3 + x2 y dy = 0
by hand. Show your steps. Check via deSolve if
desired.
1. Solve the initial value problem
cost
ty + 2y =
,
t
y (/2
MATH 308, Summer 2014
MIDTERM I
FIRST NAME(print):
LAST NAME(print):
DIRECTIONS:
1. The use of a calculator, laptop or computer is prohibited.
2. TURN OFF cell phones and put them away. If a cell phone is seen during the exam, your exam will be collected
Spring 2014 Math 308-503
Exam 1C: Solutions
c Art Belmonte
Sat, 08/Feb
3. Sketch a direction eld for the differential equation
1
y = (y + 1)2 y2 16
8
and classify any equilibrium solutions.
1. Solve the differential equation
y 2y = 3et
by hand. Show your
Spring 2014 Math 308-502
Exam 1B: Solutions
c Art Belmonte
Sat, 08/Feb
3. Sketch a direction eld for the differential equation
y =
1
(y + 1)2 y2 16
8
and classify any equilibrium solutions.
1. Solve the differential equation
y + y = tet + 1
by hand. Show
Spring 2014 Math 308-503
Exam 1D: Solutions
c Art Belmonte
Sat, 08/Feb
y + 2ty = 2tet
2
by hand. Show your steps. Give an explicit solution
for your nal answer. Check via deSolve if desired.
The differential equation is linear and in
standard linear form
Spring 2014 Math 308-503
Exam 3D: Solutions
c Art Belmonte
Fri, 04/Apr
y (0) = 1
y (0) = 2,
via the Laplace transform method.
(s) (2) + (1) (1) + 3
Y (s) =
2
s2 + 22
s2 + 4
s
1
6
2 23
2
Y (s) = 2 2
2
+ 4
s + 22 2 s + 22 2 (s2 + 22 )2
1
2
t
2
or
y (t) +
Spring 2014 Math 308-503
Exam 2D: Solutions
c Art Belmonte
Fri, 14/Mar
1. Solve the Cauchy-Euler equation and show steps.
t 2 y + 0ty 2y = 0,
t > 0.
Here is the books method. We identiy a = 1,
b = 0, c = 2. Then b a = 0 1 = 1.
Let t = ez or z = lnt. Thi
Spring 2014 Math 308-502
Exam 1A: Solutions
c Art Belmonte
Sat, 08/Feb
y + 3y = t + e2t
by hand. Show your steps. Give an explicit solution
for your nal answer. Check via deSolve if desired.
The differential equation is linear and in
standard linear form
Spring 2013 Math 308-503
Exam 3A: Solutions
c Art Belmonte
Sun, 07/Apr
1. Compute the following using linearity, algebraic
manipulation, partial fraction expansion, and/or
table lookup.
(a) the Laplace transform of f (t) = 2t 2 + 3t sin 5t
L cfw_ f (t) =
Spring 2014 Math 308-502
Exam 3A: Solutions
c Art Belmonte
Fri, 04/Apr
y (0) = 0,
y (0) = 2
via the Laplace transform method.
(s) (0) + (1) (2) +
Y (s) =
Y (s) =
y (t) =
2
s3
s2 + 4
s
2
1 1 1 1 2
1
+
+
8 s2 + 22 s2 + 22 8 s 2 2 s3
1
1
1 2
8 cos 2t + sin
Spring 2013 Math 308-503
Exam 4A: Solutions
c Art Belmonte
Fri, 26/Apr
2. Find a general solution of the system x = Ax,
1 1
. Show your steps.
where A =
1
3
Compute the eigenvalues of A.
1. Find a general solution of the
system x = Ax,
2 4 3
where A = 3
Spring 2013 Math 308-503
Exam 2A: Solutions
c Art Belmonte
Fri, 15/Mar
1. Find a general solution of the differential equation
y 6y + 25y = 0 by hand. (Check with deSolve.)
The characteristic equation is r2 6r + 25 = 0.
6 36 100
= 3 4i.
Its roots are r =
Spring 2013 Math 308-503
Exam 4B: Solutions
c Art Belmonte
Fri, 26/Apr
2. Find a general solution of the system x = Ax,
7 1
. Show your steps.
where A =
1
5
Compute the eigenvalues of A.
1. Find a general solution of the system x = Ax,
1 1
4
2 1 . Show y
NAME:
MATH 308
July 30, 2014
QUIZ 3
GOOD LUCK
Show all your work and indicate your nal answer clearly. You will be graded not merely
on the nal answer, but also on the work leading up to it.
1. Solve (use the method of undetermined coecients)
y + y = ex
MATH 308, Summer 2014
MIDTERM II
FIRST NAME(print):
LAST NAME(print):
DIRECTIONS:
1. The use of a calculator, laptop or computer is prohibited.
2. TURN OFF cell phones and put them away. If a cell phone is seen during the exam, your exam
will be collected
NAME:
MATH 308
August 7, 2014
QUIZ 4
GOOD LUCK
Show all your work and indicate your nal answer clearly. You will be graded not merely
on the nal answer, but also on the work leading up to it.
1. Solve (use the Laplace transform)
y + 4y + 5y = (t 2),
key:
NAME:
MATH 308
July 24, 2014
QUIZ 2
GOOD LUCK
Show all your work and indicate your nal answer clearly. You will be graded not merely
on the nal answer, but also on the work leading up to it.
1-3. Solve the following dierential equations.
1.
2y 5y 3y = 0
NAME:
MATH 308
July 16, 2014
QUIZ 1
GOOD LUCK
Show all your work and indicate your nal answer clearly. You will be graded not merely
on the nal answer, but also on the work leading up to it.
1. (2 points) State whether the given dierential equation is li
Spring 2013 Math 308-503
Exam 2B: Solutions
c Art Belmonte
Fri, 15/Mar
1. Find a general solution of the differential equation
y + 2y + 9y = 0 by hand. (Check with deSolve.)
The characteristic equation is r2 + 2r + 9 = 0.
2 4 36
Its roots are r =
= 1 2 2
Spring 2013 Math 308-503
Exam 3B: Solutions
c Art Belmonte
Sun, 07/Apr
1. Compute the following using linearity, algebraic
manipulation, partial fraction expansion, and/or
table lookup.
(a) the Laplace transform of f (t) = 3t 2 + 2t cos 7t
L cfw_ f (t) =